{"id":4585,"date":"2023-02-21T09:35:46","date_gmt":"2023-02-21T09:35:46","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=4585"},"modified":"2023-02-21T09:38:58","modified_gmt":"2023-02-21T09:38:58","slug":"ncert-solutions-class-9-maths-chapter-13-surface-areas-and-volumes-ex-13-5","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-13-surface-areas-and-volumes-ex-13-5\/","title":{"rendered":"NCERT Solutions Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.5"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 9 Maths\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 13 (Surface Areas and Volumes)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 9 Mathematics\u00a0<strong>Chapter &#8211; 13 Surface Areas and Volumes <\/strong>Exercise 13.5 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Chapter 13: Surface Areas and Volumes<\/strong><\/span><\/p>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-13-surface-areas-and-volumes-ex-13-1\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 13.1<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-13-surface-areas-and-volumes-ex-13-2\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 13.2<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-13-surface-areas-and-volumes-ex-13-3\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 13.3<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-13-surface-areas-and-volumes-ex-13-4\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 13.4<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-13-surface-areas-and-volumes-ex-13-6\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 13.6<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-13-surface-areas-and-volumes-ex-13-7\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 13.7<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-13-surface-areas-and-volumes-ex-13-8\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 13.8<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-13-surface-areas-and-volumes-ex-13-9\/\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 13.9<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 13.5<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. A matchbox measures 4 cm\u00d72.5 cm\u00d71.5 cm. What will be the volume of a packet containing 12 such boxes?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\n<\/strong>Length of the matchbox, <em>l<\/em> = 4 cm,<br \/>\nBreadth of the matchbox, <em>b<\/em> = 2.5 cm,<br \/>\nHeight of the matchbox, <em>h<\/em> = 1.5 cm<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4660\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-13.5-Ans01.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"496\" height=\"372\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-13.5-Ans01.png 551w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-13.5-Ans01-300x225.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-13.5-Ans01-480x360.png 480w\" sizes=\"auto, (max-width: 496px) 100vw, 496px\" \/><br \/>\nThe volume of each matchbox = <em>l \u00d7 b \u00d7 h<\/em> <\/span><br \/>\n<span style=\"color: #000000;\">= 4 cm \u00d7 2.5 cm \u00d7 1.5 cm<\/span><br \/>\n<span style=\"color: #000000;\">= 15 cm<sup>3<br \/>\n<\/sup>Volume of 12 matchboxes = 12 \u00d7 15cm<sup>3<\/sup>\u00a0= 180cm<sup>3<br \/>\n<\/sup>Thus, the volume of the\u00a0packet containing 12 such matchboxes is 180 cm<sup>3<\/sup>.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. A cuboidal water tank is 6 m long, 5 m wide and 4.5 m deep. How many litres of water can it hold? (1 m<sup>3\u00a0<\/sup>= 1000 l)<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\n<\/strong>Length of the cuboidal tank, <em>l<\/em> = 6 m, <\/span><br \/>\n<span style=\"color: #000000;\">Breadth of the cuboidal tank, <em>b<\/em> = 5 m, <\/span><br \/>\n<span style=\"color: #000000;\">Height of the cuboidal tank, <em>h<\/em> = 4.5 m<\/span><br \/>\n<span style=\"color: #000000;\">Volume of the cuboidal tank = <em>l \u00d7 b \u00d7 h<br \/>\n<\/em>V = 6m \u00d7 5m \u00d7 4.5m<\/span><br \/>\n<span style=\"color: #000000;\">V = 135 m<sup>3<br \/>\n<\/sup>V = 135 \u00d7 1000L<\/span><br \/>\n<span style=\"color: #000000;\">V = 135000L (1m<sup>3<\/sup>\u00a0= 1000L)<\/span><br \/>\n<span style=\"color: #000000;\">Thus, the cuboidal water tank can hold 135000 litres of water.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. A cuboidal vessel is 10 m long and 8 m wide. How high must it be made to hold 380 cubic metres of a liquid?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\n<\/strong>Let the height of the cuboidal vessel = <em>h<br \/>\n<\/em>Length of the cuboidal vessel, <em>l<\/em> = 10 m<\/span><br \/>\n<span style=\"color: #000000;\">The breadth of the cuboidal vessel, <em>b<\/em> = 8 m<\/span><br \/>\n<span style=\"color: #000000;\">The capacity of the cuboidal vessel (V) = 380 m<sup>3<br \/>\n<\/sup>Volume of the liquid in the cuboidal vessel = <em>l\u00a0\u00d7 b\u00a0\u00d7 h<br \/>\n<\/em>l\u00a0\u00d7 b\u00a0\u00d7 h = 380m<sup>3<br \/>\n<\/sup>10 m \u00d7 8 m\u00a0\u00d7 h = 380m<sup>3<br \/>\n<\/sup>h = 380 \/ (10\u00a0\u00d7 8)<\/span><br \/>\n<span style=\"color: #000000;\">h = 4.75 m<\/span><br \/>\n<span style=\"color: #000000;\">Thus, the cuboidal vessel must be made 4.75 m high.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4. Find the cost of digging a cuboidal pit of 8 m long, 6 m broad and 3 m deep at the rate of Rs. 30 per m<sup>3<\/sup>.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\n<\/strong>Length of the cuboidal pit, <em>l<\/em> = 8 m<\/span><br \/>\n<span style=\"color: #000000;\">Breadth of the cuboidal pit, <em>b<\/em> = 6 m<\/span><br \/>\n<span style=\"color: #000000;\">Height of the cuboidal pit, <em>h<\/em> = 3 m<\/span><br \/>\n<span style=\"color: #000000;\">Volume of the cuboidal\u00a0pit = <em>l \u00d7 b \u00d7 h<br \/>\n<\/em>= 8m \u00d7 6m \u00d7 3m<\/span><br \/>\n<span style=\"color: #000000;\">= 144 m<sup>3<br \/>\n<\/sup>Thus, the cost of digging the pit at \u20b9 30 per m<sup>3<\/sup>\u00a0=\u00a0\u20b9 30 \u00d7 144 = \u20b9 4320<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>5. The capacity of a cuboidal tank is 50000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\n<\/strong>Let the breadth of the cuboidal tank = <em>b<\/em><\/span><br \/>\n<span style=\"color: #000000;\">Length of the cuboidal tank, <em>l<\/em> = 2.5 m<\/span><br \/>\n<span style=\"color: #000000;\">Height of the cuboidal tank, <em>h<\/em> = 10 m<\/span><br \/>\n<span style=\"color: #000000;\">The capacity of the tank = 50000L <\/span><br \/>\n<span style=\"color: #000000;\">= 50000\/1000 m<sup>3<\/sup>\u00a0(\u2235 1m<sup>3<\/sup>\u00a0= 1000L)<\/span><br \/>\n<span style=\"color: #000000;\">= 50 m<sup>3<br \/>\n<\/sup>Volume of the cuboidal tank =\u00a0<em>l \u00d7 b \u00d7 h<br \/>\n<\/em>l \u00d7 b \u00d7 h = 50 m<sup>3<br \/>\n<\/sup>b = 50 m<sup>3<\/sup>\/l \u00d7 h<\/span><br \/>\n<span style=\"color: #000000;\">b = 50 m<sup>3<\/sup>\/(2.5m \u00d7 10m)<\/span><br \/>\n<span style=\"color: #000000;\">= 2 m<\/span><br \/>\n<span style=\"color: #000000;\">Therefore, the breadth of the tank is 2 m.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>6. A village, having a population of 4000, requires 150 litres of water per head per day. <\/strong><strong>It has a tank measuring 20 m\u00d715 m\u00d76 m. For how many days will the water in this tank last?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\n<\/strong>Length of the tank, <em>l<\/em> = 20 m<br \/>\nBreadth of the tank, <em>b<\/em> = 15 m<br \/>\nHeight of the tank, <em>h<\/em> = 6 m<br \/>\nThe volume of the water in the tank = <em>l \u00d7 b \u00d7 h<br \/>\n<\/em>= 20m \u00d7 15m \u00d7 6m<\/span><br \/>\n<span style=\"color: #000000;\">= 1800 m<sup>3<br \/>\n<\/sup>Total population of the village = 4000<br \/>\nRequirement of water per head per day is\u00a0150 litres.<\/span><br \/>\n<span style=\"color: #000000;\">Requirement of water per day for 4000 population = 4000 \u00d7 150L<\/span><br \/>\n<span style=\"color: #000000;\">= 600000L<\/span><br \/>\n<span style=\"color: #000000;\">= 600000\/1000 m<sup>3<\/sup>\u00a0 (\u2235 1000L = 1 m<sup>3<\/sup>)<\/span><br \/>\n<span style=\"color: #000000;\">= 600 m\u00b3<\/span><br \/>\n<span style=\"color: #000000;\">Number of days for which the water of the tank will last = 1800m<sup>3<\/sup>\/600m<sup>3<\/sup>\u00a0= 3 days<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>7. A godown measures 40 m\u00d725 m\u00d715 m. Find the maximum number of wooden crates, each <\/strong><strong>measuring 1.5m \u00d7 1.25 m \u00d7 0.5 m, that can be stored in the godown.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\n<\/strong>Length of the godown, <em>L <\/em>= 40 m<br \/>\nBreadth, <em>B <\/em>= 25 m<br \/>\nHeight, <em>H <\/em>= 15 m<br \/>\nCapacity of the godown = <em>L\u00a0\u00d7 B\u00a0\u00d7 H<br \/>\n<\/em>= 40m \u00d7 25m \u00d7 15m<\/span><br \/>\n<span style=\"color: #000000;\">= 15000 m<sup>3<br \/>\n<\/sup>Length of the crate, <em>l<\/em> = 1.5 m<\/span><br \/>\n<span style=\"color: #000000;\">Breadth of the crate, <em>b<\/em> =1.25 m<\/span><br \/>\n<span style=\"color: #000000;\">Height of the crate, <em>h<\/em> = 0.5 m<\/span><br \/>\n<span style=\"color: #000000;\">Volume of each crate =\u00a0<em>l \u00d7 b \u00d7 h<br \/>\n<\/em>= 1.5m \u00d7 1.25m \u00d7 0.5m<\/span><br \/>\n<span style=\"color: #000000;\">= 0.9375 m<sup>3<br \/>\n<\/sup>Number of crates = 15000m<sup>3<\/sup>\/0.9375m<sup>3<\/sup>\u00a0= 16000<\/span><br \/>\n<span style=\"color: #000000;\">The maximum number of wooden crates that can be stored in the godown is 16000.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>8. A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube? Also, find the ratio between their surface areas.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\n<\/strong>Side of the cube = 12 cm<br \/>\nThe volume of the solid cube = a<sup>3<br \/>\n<\/sup>= (12 cm)<sup>3<br \/>\n<\/sup>= 1728 cm<sup>3<br \/>\n<\/sup>The cube is cut into 8 equal cubes of the same volume.<\/span><br \/>\n<span style=\"color: #000000;\">Volume of each small cube = (1\/8) \u00d7 1728 cm<sup>3<\/sup>\u00a0= 216 cm<sup>3<br \/>\n<\/sup>Let &#8216;x&#8217; be the side of each small cube. <\/span><br \/>\n<span style=\"color: #000000;\">Volume of each small cube = x<sup>3<\/sup>\u00a0= 216 cm<sup>3<br \/>\n<\/sup>x<sup>3<\/sup>\u00a0= (6 cm)<sup>3<\/sup>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 [Since 6<sup>3<\/sup>\u00a0= 216]<\/span><br \/>\n<span style=\"color: #000000;\">x = 6 cm<\/span><br \/>\n<span style=\"color: #000000;\">Surface area of the solid cube = 6a<sup>2<br \/>\n<\/sup>Surface area of the small cube = 6x<sup>2<br \/>\n<\/sup><\/span><span style=\"color: #000000;\">Ratio\u00a0between their surface areas = 6a<sup>2<\/sup>\/6x<sup>2<br \/>\n<\/sup>= a<sup>2<\/sup>\/x<sup>2<br \/>\n<\/sup>= (a\/x)<sup>2<br \/>\n<\/sup>=\u00a0(12\/6)<sup>2<br \/>\n<\/sup>= 4\/1 <\/span><br \/>\n<span style=\"color: #000000;\">The side of the new cube is 6 cm and the\u00a0ratio between the surface areas is 4 : 1.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>9. A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<br \/>\n<\/strong>Width of the river,\u00a0<em>b<\/em> = 40 m<\/span><br \/>\n<span style=\"color: #000000;\">Depth of the river,\u00a0<em>h<\/em> = 3 m<\/span><br \/>\n<span style=\"color: #000000;\">Flowing rate of water = 2 km \/ h<\/span><br \/>\n<span style=\"color: #000000;\">= 2000 m \/ 60 min<\/span><br \/>\n<span style=\"color: #000000;\">= 100\/3 m\/min<\/span><br \/>\n<span style=\"color: #000000;\">Length of the water flowing in 1 minute, <em>l<\/em> = 100\/3 m<\/span><br \/>\n<span style=\"color: #000000;\">The volume of the water that falls into the sea in 1 minute = <em>l \u00d7 b \u00d7 h<br \/>\n<\/em>= 100\/3 m \u00d7 40 m \u00d7 3 m<\/span><br \/>\n<span style=\"color: #000000;\">= 4000 m<sup>3<br \/>\n<\/sup>Thus, 4000 m<sup>3<\/sup>\u00a0of water will fall into the sea in a minute<\/span><\/p>\n<p style=\"text-align: justify;\">\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 9 Maths\u00a0 Chapter &#8211; 13 (Surface Areas and Volumes)\u00a0 The NCERT Solutions in English Language for Class 9 Mathematics\u00a0Chapter &#8211; 13 Surface Areas and Volumes Exercise 13.5 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 13: Surface Areas and Volumes NCERT Solution Class 9 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[698],"tags":[725,702,186,726,701,5],"class_list":["post-4585","post","type-post","status-publish","format-standard","hentry","category-class-9-maths","tag-class-9th-chapter-13-surface-areas-and-volumes-in-english","tag-ncert-solution-class-9","tag-ncert-solutions","tag-ncert-solutions-class-9-maths-chapter-13-in-english","tag-ncert-solutions-class-9-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - 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