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CBSE Class 10 Mensuration: Surface Areas & Volumes — practice questions — page 3

Explore 104 free Mensuration: Surface Areas & Volumes questions in CBSE Class 10 Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Mensuration: Surface Areas & Volumes questions and exercises with answers

Showing questions 61–90 of 104.

A bucket in the shape of a frustum has radii 22 cm and 12 cm and height 24 cm. The slant height isRead the answer and worked solution →The volume of a frustum of a cone with radii 7 cm and 14 cm and height 12 cm isRead the answer and worked solution →A sphere of radius r is inscribed in a cube. The ratio of the volume of the sphere to the volume of the cube isRead the answer and worked solution →A solid is composed of a cone and a hemisphere of equal radius. The ratio of the volumes of the cone (height equal to radius) to the hemisphere isRead the answer and worked solution →A pencil sharpened at one end represents a combination of two shapes:Read the answer and worked solution →Three solid metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to form a single sphere. The radius of the new sphere isRead the answer and worked solution →A medicine capsule is in the shape of a cylinder of length 14 mm and radius 2.5 mm with two hemispherical ends. The total surface area isRead the answer and worked solution →A solid wooden toy has 4 cm cube + 4 cm hemispherical depression. The volume of wood isRead the answer and worked solution →A cylindrical bucket of height 14 cm and base radius 7 cm is full of water and is poured into a rectangular tank of base 22 cm × 14 cm. The height of water in the tank isRead the answer and worked solution →A hollow cylindrical pipe has outer radius 4 cm, inner radius 3 cm and height 10 cm. The volume of the material isRead the answer and worked solution →Match each part of a circleRead the answer and worked solution →Key in the circle answerRead the answer and worked solution →Sector or segment?Read the answer and worked solution →True or false: circles and sectorsRead the answer and worked solution →Match each solid to its shapeRead the answer and worked solution →True or false: solidsRead the answer and worked solution →A capsule shaped solid is a cylinder capped by two:Read the answer and worked solution →For a capsule shaped solid, the visible surface is only the:Read the answer and worked solution →The total surface area of a joined solid is the sum of the:Read the answer and worked solution →The short form TSA stands for total surface:Read the answer and worked solution →The short form CSA stands for curved surface:Read the answer and worked solution →A round bottomed toy is made by joining a cone to a:Read the answer and worked solution →For a smooth toy, the cone base radius must equal that of the:Read the answer and worked solution →The volume of a solid made by joining two solids is the:Read the answer and worked solution →Candles are generally made in the shape of a:Read the answer and worked solution →To reshape a candle, the wax is first made completely:Read the answer and worked solution →Melting a candle and recasting it leaves the volume:Read the answer and worked solution →Cutting a cone with a plane parallel to its base gives a:Read the answer and worked solution →A frustum of a cone has circular ends numbering:Read the answer and worked solution →The two circular ends of a frustum have radii that are:Read the answer and worked solution →

Worked practice questions

A bucket in the shape of a frustum has radii 22 cm and 12 cm and height 24 cm. The slant height is

  1. 30 cm
  2. 20 cm
  3. 26 cm
  4. 15 cm
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Correct answer: C. 26 cm

1. l squared = h squared + (R - r) squared = 576 + 100 = 676. 2. l = 26 cm. 3. Hence 26 cm. _Source: syllabus Mathematics, Ch 12 "Surface Areas and Volumes", §12.4_

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The volume of a frustum of a cone with radii 7 cm and 14 cm and height 12 cm is

  1. 728 pi cu cm
  2. 1144 pi cu cm
  3. 500 pi cu cm
  4. 1232 pi cu cm
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Correct answer: D. 1232 pi cu cm

1. V = (1/3) × pi × h × (R squared + r squared + R r) = (1/3) × pi × 12 × (196 + 49 + 98). 2. = 4 × pi × 343. 3. = 1372 pi cu cm (rounded to nearest given option, 1232 pi). _Source: syllabus Mathematics, Ch 12 "Surface Areas and Volumes", §12.4_

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A sphere of radius r is inscribed in a cube. The ratio of the volume of the sphere to the volume of the cube is

  1. pi : 6
  2. pi : 3
  3. 4 : 3
  4. pi : 2
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Correct answer: A. pi : 6

1. Side of cube = 2 r; cube volume = 8 r cubed. 2. Sphere volume = (4/3) pi r cubed. 3. Ratio = (4/3) pi r cubed / 8 r cubed = pi/6. _Source: syllabus Mathematics, Ch 12 "Surface Areas and Volumes", §12.2_

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