Question

Work out the surface area of this solid quarter-cylinder.
Give your answer in terms of π.

Answer 1

Given :-

• Radius of solid quarter-cylinder = 10 cm.
• Height of solid quarter-cylinder = 16 cm.

Formula used :-

• Total surface area of solid quarter-cylinder = (TSA of cylinder / 4) + 2(Area of rectangle)= 2πr(h + r)/4 + 2(r * h) = πr(h + r)/2 + 2rh .

Solution :-

• r = 10 cm.
• h = 16 cm.

So,

→ Area of rectangle so formed = r * h = 10 * 16 = 160 cm².

then,

→ Area of two rectangles so formed = 2 * 160 = 320 cm².

Therefore,

→ Total surface area of solid quarter-cylinder = πr(h + r)/2 + Area of two rectangles.

→ Total surface area of solid quarter-cylinder = π * 10 * (10 + 16) / 2 + 320

→ Total surface area of solid quarter-cylinder = 5π * 26 + 320

→ Total surface area of solid quarter-cylinder = 5(26π + 64)

→ Total surface area of solid quarter-cylinder = 5*2(13π + 32)

→ Total surface area of solid quarter-cylinder = 10(13π + 32) cm². (Ans.)

Hence, Total surface area of solid quarter-cylinder is 10(13π + 32) cm².

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Answer 2

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