{"id":7546,"date":"2021-03-16T15:22:14","date_gmt":"2021-03-16T09:52:14","guid":{"rendered":"https:\/\/apboardsolutions.guru\/?p=7546"},"modified":"2021-09-15T11:38:56","modified_gmt":"2021-09-15T06:08:56","slug":"ap-board-8th-class-maths-solutions-chapter-14-ex-14-2","status":"publish","type":"post","link":"https:\/\/apboardsolutions.guru\/ap-board-8th-class-maths-solutions-chapter-14-ex-14-2\/","title":{"rendered":"AP Board 8th Class Maths Solutions Chapter 14 Surface Areas and Volumes Ex 14.2"},"content":{"rendered":"

AP State Syllabus AP Board 8th Class Maths Solutions<\/a> Chapter 14 Surface Areas and Volumes Ex 14.2 Textbook Questions and Answers.<\/p>\n

AP State Syllabus 8th Class Maths Solutions 14th Lesson Surface Areas and Volumes Exercise 14.2<\/h2>\n

\"AP<\/p>\n

Question 1.
\nFind the volume of the cuboid whose dimensions are given below.
\n\"AP
\nSolution:
\n\"AP<\/p>\n

Question 2.
\nFind the capacity of the tanks with the following internal dimensions. Express the capacity in cubic meters and litres for each tank.
\n\"AP
\nSolution:
\n\"AP<\/p>\n

\"AP<\/p>\n

Question 3.
\nWhat will happen to the volume of a cube if the length of its edge is reduced to half? Is the volume get reduced? If yes, how much?
\nSolution:
\nVolume of a cube of side (s) is V1<\/sub> = a3<\/sup>
\nIf the length of the side is reduced by half then
\ns = \\(\\frac{\\mathrm{a}}{2}\\)
\n\u2234 Volume of cube (V2<\/sub> ) = s3<\/sup>
\n\"AP
\n\u2234 V2<\/sub> = \\(\\frac { 1 }{ 8 }\\) \u00d7 V1<\/sub>
\n\u2234 V1<\/sub> = 8V2<\/sub><\/p>\n

\"AP<\/p>\n

Question 4.
\nFind the volume of each of the cube whose sides are.
\n(i) 6.4 cm
\n(ii) 1.3 m
\n(iii) 1.6 m.
\nSolution:
\nVolume of a cube(V) = a3<\/sup><\/p>\n

i) a = 6.4 cm
\nii) a = 1.3 m
\niii) a = 1.6 m<\/p>\n

V = (6.4)3
\n<\/sup>Volume of a cube (V) = a3
\n<\/sup>= 6.4 \u00d7 6.4 \u00d7 6.4
\n= 262.144 cm3
\n<\/sup><\/p>\n

V = (1.3)3<\/sup>
\n= 1.3 \u00d7 1.3 \u00d7 1.3
\n= 2.197 m3
\n<\/sup><\/p>\n

V = (1.6)3<\/sup>
\n= 1.6 \u00d7 1.6 \u00d7 1.6
\n= 4.096 m3<\/sup><\/p>\n

\"AP<\/p>\n

Question 5.
\nHow many bricks will be required to build a wall of 8 m long, 6m height and 22.5 cm thici if each brick measures 25 cm by 11.25 cm by 6 cm?
\nSolution:
\nThe volume of a wall of measures
\n8 m \u00d7 22.5 cm \u00d7 6 m
\n(V1<\/sub>) = l1<\/sub>b1<\/sub>h1<\/sub>
\n= 8 m \u00d7 22.5 cm \u00d7 6 m
\n= 800 cm \u00d7 22.5 cm \u00d7 600 cm
\nThe volume of a brick each measures
\n25 cm \u00d7 11.25 cm \u00d7 6 cm
\n(V2<\/sub>) = l2<\/sub>b2<\/sub>h2<\/sub>
\n= 25 \u00d7 11.25 \u00d7 6 cm3<\/sup>
\n\u2234 The no.of bricks will be required
\n\"AP
\n= 32 \u00d7 2 \u00d7 100 = 6400<\/p>\n

Question 6.
\nA cuboid is 25 cm long, 15 cm broad, and 8 cm high . How much of its volume will differ from that of a cube with the edge of 16 cm\u2019?
\nSolution:
\nVolume of a cuboid (V1<\/sub>) of measures
\n= 25 cm, b = 15 cm, h = 8 cm.
\nV1<\/sub> = 25 \u00d7 15 \u00d7 8 = 3000 cm3<\/sup>
\nVolume of a cube of measure side (s) = 16 cm is
\nV2<\/sub> = (s)3<\/sup> = (16)3<\/sup> = 16 \u00d7 16 \u00d7 16
\n= 4096 cm3<\/sup>
\nThe difference between their volumes
\n= V2<\/sub> – V1<\/sub>
\n= 4096 – 3000
\n= 1096 cm3<\/sup><\/p>\n

\"AP<\/p>\n

Question 7.
\nA closed box is made up of wood which is 1cm thick .The outer dimensions of the box is 5 cm \u00d7 4 cm \u00d7 7 cm. Find the volume of the wood used.
\nSolution:
\nThe volume of a box formed with outer measures 5 cm \u00d7 4 cm \u00d7 7 cm
\nV1<\/sub> = l \u00d7 b \u00d7 h
\n= 5 \u00d7 4 \u00d7 7
\n\u2234 V1<\/sub> = 140 cm3<\/sup>
\nInner measures
\n= l – 2w, b – 2w, h – 2w
\n= (5 – 2 \u00d7 1), (4 – 2 \u00d7 1), (7 – 2 \u00d7 1)
\n= (5 – 2), (4 – 2), (7 – 2)
\n= 3 cm, 2 cm, 5 cm
\n\u2234 Volume of a box formed with inner measures
\nV2<\/sub> = (l – 2w)(b – 2w)(h – 2w)
\n= 3 \u00d7 2 \u00d7 5 = 30 cm3<\/sup>
\n\u2234 The volume of wood used = V1<\/sub> – V2<\/sub>
\n= 140 – 30 = 110 cm3<\/sup><\/p>\n

\"AP<\/p>\n

Question 8.
\nHow many cubes of edge 4cm, each can be cut out from cuboid whose length, breadth and height are 20 cm, 18 cm and 16 cm respectively
\nSolution:
\nThe volume of a cuboid formed with the measures 20 cm \u00d7 18 cm \u00d7 16 cm
\n(V1<\/sub>) = l1<\/sub>b1<\/sub>h1<\/sub> = 20 \u00d7 18 \u00d7 16
\nVolume of a cube (V2<\/sub>) = s3<\/sup>
\ns = 4 cm (given)
\n\u2234 V2<\/sub> = (s)3<\/sup> = (4)3<\/sup>= 4 \u00d7 4 \u00d7 4 cm3<\/sup>
\n\u2234 No.of cubes are required
\n= \\(\\frac{V_{1}}{V_{2}}=\\frac{20 \\times 18 \\times 16}{4 \\times 4 \\times 4}\\)
\n= 90<\/p>\n

Question 9.
\nHow many cuboids of size 4 cm \u00d7 3 cm \u00d7 2 cm can be made from a cuboid of size 12 cm x 9cm x 6cm?
\nSolution:
\nVolume of a cuboid of measures 12 cm \u00d7 9 cm \u00d7 6 cm
\nV1<\/sub> = l \u00d7 b \u00d7 h = 12 \u00d7 9 \u00d7 6
\nVolume of the smaller cuboid of measures 4 cm \u00d7 3 cm \u00d7 2 cm
\nV2<\/sub> = l2<\/sub>b2<\/sub>h2<\/sub> = 4 \u00d7 3 \u00d7 2
\n\u2234 No.of cuboids are made
\n= \\(\\frac{V_{1}}{V_{i}}=\\frac{12 \\times 9 \\times 6}{4 \\times 3 \\times 2}\\) = 27<\/p>\n

Question 10.
\nA vessel in the shape of a cuboid is 30 cm long and 25 cm wide. What should be its height to hold 4.5 litres of water ?
\nSolution:
\nLength of a cuboidal vessel (l) = 30 cm
\nbreadth (b) = 25 cm
\nheight (h) = ?
\nThe volume of water m a cuboidal vessel = 4.5 Lts.
\n= 4.5 \u00d7 1000 cm3<\/sup>
\n= 4500 cm3<\/sup>
\n\u2234 l \u00d7 b \u00d7h = 4500
\n\u21d2 30 \u00d7 25 \u00d7 h = 4500
\n\u21d2 h = \\(\\frac{4500}{30 \\times 25}\\)
\n\u2234 h = 6 cm
\n\u2234 Height of the vessel (h) = 6 cm<\/p>\n","protected":false},"excerpt":{"rendered":"

AP State Syllabus AP Board 8th Class Maths Solutions Chapter 14 Surface Areas and Volumes Ex 14.2 Textbook Questions and Answers. AP State Syllabus 8th Class Maths Solutions 14th Lesson Surface Areas and Volumes Exercise 14.2 Question 1. Find the volume of the cuboid whose dimensions are given below. Solution: Question 2. Find the capacity …<\/p>\n","protected":false},"author":4,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/7546"}],"collection":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/users\/4"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/comments?post=7546"}],"version-history":[{"count":0,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/posts\/7546\/revisions"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/media?parent=7546"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/categories?post=7546"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.guru\/wp-json\/wp\/v2\/tags?post=7546"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}