The circumference of the base of a right circular cone is 44 7 cm and its slant height
is 28 cm. Find the volume of the cone.
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EXPLANATION.
Circumference of the base of the cone is 44√7 cm.
It's slant height is 28 cm.
As we know that,
Formula of :
Circumference of the base = 2πr.
Slant height (l) : l² = r² + h².
Using this formula in this question, we get.
⇒ 2πr = 44√7.
⇒ 2 x 22/7 x r = 44√7.
⇒ 44/7 x r = 44√7.
⇒ r/7 = √7.
⇒ r = 7√7 cm.
Radius of cone is 7√7 cm.
⇒ l² = r² + h².
⇒ (28)² = (7√7)² + h².
⇒ 784 = 343 + h².
⇒ h² = 441.
⇒ h = 21 cm.
Height of cone is 21 cm.
To find : The volume of cone.
Volume of cone = 1/3πr²h.
⇒ 1/3 x 22/7 x (7√7)² x 21.
⇒ 1/3 x 22/7 x 343 x 21.
⇒ (22 x 343 x 21)/(21).
⇒ 22 x 343 = 7546 cm³.
∴ Volume of cone is 7546 cm³.
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