CLASS 10 MATHS · SURFACE AREAS AND VOLUMES

Surface area and volume of combined solids

Add the parts that are actually exposed (for surface area) or the volumes of all parts. Use π = 22/7.

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Worked examples

Example 1 · level 1

A medicine capsule is a cylinder of length 8 mm with a hemisphere of radius 7 mm on each end. Find its total surface area (in mm²). Use π = 22/7.

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Cylinder side = 2 × 22/7 × 7 × 8 = 352.
Two hemispheres = 4 × 22/7 × 49 = 616.
Total = 968 mm².

Answer: 968

Example 2 · level 2

A tent at a wedding is a cylinder of radius 21 m and height 4 m with a cone of the same radius and slant height 29 m on top. How much canvas is needed (in m²)? Use π = 22/7.

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Cylinder side = 2 × 22/7 × 21 × 4 = 528.
Cone = 22/7 × 21 × 29 = 1914.
Canvas = 2,442 m².

Answer: 2,442

Example 3 · level 3

A solid is a cone of radius 21 cm and height 20 cm on top of a hemisphere of the same radius. Find its volume (in cm³, to 2 decimal places if needed). Use π = 22/7.

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Cone = 9,240 cm³.
Hemisphere = ⅔ × 22/7 × 9261 = 19,404 cm³.
Total = 28,644 cm³.

Answer: 28,644