The radius and slant height of a right circular cone are 5 cm and 13 cm respectively. What is the volume of the cone?a)100π cm3b)50π cm3c)65π cm3d)169 cm3Correct answer is option 'A'. Can you explain this answer?

Question

The radius and slant height of a right circular cone are 5 cm and 13 cm respectively. What is the volume of the cone?a)100&pi; cm3b)50&pi; cm3c)65&pi; cm3d)169 cm3Correct answer is option 'A'. Can you explain this answer?

Answer

Sol:- Given radius r=5 cm,slant height l= 13 cm,
we know that volume of a cone is v=1/3 πr^2h
l=√r^2+h^2;
l^2=r^2+h^2
169=25+h^2
h=12
v=1/3π*25*12
v=100π cm^3

Answer

In a cone h = √(l² – r²) = √(13² – 5²) = 12cm
Volume of the cone = 1/3 × π r² h
⇒ 1/3 × π × 5² × 12
⇒ 100π cm³

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