Question

40) A cone is surmounted on a hemisphere. The slant height of the cone

is 7cm and its radius is 5cm, then total surface area of the solid is.

A) 400cm2 B) 440cm2 C) 380cm2 D) 350cm2​

Answer 1

Given : A cone is surmounted on a hemisphere. The slant height of the cone is 7cm and its radius is 5cm,

To Find :  total surface area of the solid

Solution:

cone is surmounted on a hemisphere.

TSA = CSA hemisphere + CSA cone

CSA  hemisphere  = 2πR²  = 2π ( 5)²  = 50π  cm²

CSA cone = πRL  = π(5)(7) = 35π  cm²

total surface area of the solid  =  50π + 35π  =  85π cm²

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Answer 2

Given :- A cone is surmounted on a hemisphere. The slant height of the cone is 7cm and its radius is 5cm, then total surface area of the solid is.

Solution :-

we know that,

• CSA of cone = π * radius * slant height
• CSA of hemisphere = 2 * π * (radius)²
• When cone is surmounted on a hemisphere both have same radius .

so,

→ TSA of solid = CSA of cone + CSA of hemisphere

→ TSA of solid = πrl + 2πr²

→ TSA of solid = πrl + 2πr²

→ TSA of solid = πr(l + 2r)

→ TSA of solid = 3.14 * 5 * (7 + 2*5)

→ TSA of solid = 3.14 * 5 * 17

→ TSA of solid = 266.9 ≈ 267 cm² .

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