LIWA

Surface Areas and Volumes

CBSE Class 10 · Maths · Chapter 12

Past board exam questions

CBSE 2027 sample paper · 1 mark

Two cubes each of volume 64 cm³ are joined end to end to form a solid. The surface area of the resultant cuboid is:

  1. 192 cm²
  2. 160 cm²
  3. 96 cm²
  4. 80 cm²
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160 cm²

CBSE 2027 sample paper · 1 mark

Two cubes each of volume 64cm³ are joined end to end to form a cuboid. The total surface area of the resulting cuboid is

  1. 128 cm²
  2. 160 cm²
  3. 176 cm²
  4. 192 cm²
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160 cm²

CBSE 2027 sample paper · 5 marks

A tent is in the shape of a cylinder surmounted by a conical top. If the height and radius of the cylindrical part are 3 m and 14 m respectively, and the total height of the tent is 13.5 m, then find the area of the canvas required for making the tent, keeping a provision of 26 m² of canvas for stitching and wastage. Also, find the cost of the canvas to be purchased at the rate of ₹ 250 per m².

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Height of the conical part = 13.5 – 3 = 10.5 m; r = 14 m. Slant height l = √(142 + 10.52) = √(196 + 110.25) = √(306.25) = 17.5 m. CSA of conical part = π r l = (22)/(7) × 14 × 17.5 = 770 m². CSA of cylindrical part = 2π r h = 2 × (22)/(7) × 14 × 3 = 264 m². Canvas required = 770 + 264 + 26 = 1060 m². Cost of canvas = 1060 × ₹ 250 = ₹ 2,65,000.

CBSE 2027 sample paper · 5 marks

A solid wooden toy is in the form of a hemisphere surmounted by a cone of the same radius. The radius of hemisphere is 3.5 cm and the total wood used in making the toy is 166(5)/(6) cm³. Find the height of the conical part. Also, find the cost of painting the hemispherical part of the toy at the rate of ₹ 15 per cm².

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Let h cm be the height of the conical part; r = 3.5 cm. Volume of toy = volume of cone + volume of hemisphere: 166(5)/(6) = (1)/(3)π r2 h + (2)/(3)π r3 (1001)/(6) = (1)/(3) × (22)/(7) × (3.5)2 × h + (2)/(3) × (22)/(7) × (3.5)3 (1001)/(6) = (38.5h)/(3) + (269.5)/(3) ⇒ 500.5 = 38.5h + 269.5 ⇒ h = 6 cm. CSA of hemispherical part = 2π r2 = 2 × (22)/(7) × (3.5)2 = 77 cm². Cost of painting = 77 × ₹ 15 = ₹ 1155.

CBSE 2026 board paper · 1 mark

A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius 10 cm. Curved surface area of the cavity carved out is (use π = 3.14) (Figure: the base of the cone is the flat circular face of the hemisphere and its vertex is the lowest point of the hemisphere.)

  1. 314√(2) cm²
  2. 314 cm²
  3. (3140)/(3) cm²
  4. 3140√(2) cm²
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314√(2) cm²

CBSE 2026 board paper · 1 mark

Two wooden solid hemispheres of same radii r, are joined at a point: one is placed above the other with their curved surfaces touching at a single point, so both flat circular faces are on the outside. The total surface area of the object is :

  1. 4π r2
  2. 6π r2
  3. 3π r2
  4. 5π r2
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6π r2

CBSE 2026 board paper · 1 mark

A cylinder of radius r is surmounted on a hemisphere of same radius. If total height of the object is 13 cm, then its inner surface area is

  1. 2π r(r + 13)
  2. 13π r
  3. 2π(13 + r)2
  4. 26π r
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26π r

CBSE 2026 board paper · 1 mark

The total surface area of a solid hemisphere of radius 7 cm is

  1. 447π sq. cm
  2. 239π sq. cm
  3. 174π sq. cm
  4. 147π sq. cm
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147π sq. cm