Question

Find the volume of a right circular cone whose area of the base is 36π cm² and slant height is 10 cm.

Answer 1

Solution:

Given:


Area of base = 36π cm²


Slant height (l) = 10 cm


Area of base = πr²


36π = πr²


36 = r²


r = √36


r = √ 6× 6= 6


r = 6 cm


Slant height (l)²= r²+h²


10² = 6² + h²


100 = 36 + h²


100 -36 = h²


64 = h²


h= √ 64 = √ 8×8


h= 8 cm

height (h) = 8 cm

Volume of cone= ⅓ πr²h


= ⅓ ×( 22/7) × 6² × 8


= ⅓ × (22/7) × 36 × 8


=( 22× 12 × 8)/7


=( 22× 96 ) /7


= 2112/7 = 301.71 cm³


Volume of cone = 2112/7 = 301.71 cm³

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Hope this will help you.....