Find the volume of the right circular cone with the following dimensions:
Question:

Find the volume of the right circular cone with the following dimensions:

(a) Radius is 6 cm and the height of the cone is 7cm

(b) Radius is 3.5 cm and height is 12 cm

(c) Slant height is 21 cm and height is 28 cm

Solution:

(a) It is given that        

Radius of the cone (r) = 6 cm

Height of the cone (h) = 7 cm

Volume of a right circular cone

$=1 / 3 \pi r^{2} h$

$=1 / 3 * 3.14 * 6^{2} * 7=264 \mathrm{~cm}^{3}$

(b) It is given that:

Radius of the cone (r) = 3.5 cm

Height of the cone (h) = 12 cm

Volume of a right circular cone

$=1 / 3 \pi r^{2} h$

$=1 / 3 * 3.14 * 3.5^{2} * 12$

$=154 \mathrm{~cm}^{3}$

(c) It is given that:

Height of the cone (h) = 28 cm

Slant height of the cone (l) = 21 cm

As we know that,

$1^{2}=r^{2}+h^{2}$

$r=\sqrt{1^{2}-h^{2}}$

$r=\sqrt{28^{2}-21^{2}}=7 \sqrt{7}$

Volume of a right circular cone:

$=1 / 3 \pi r^{2} h$

$=\frac{1}{3} * 3.14 *(7 \sqrt{7})^{2} * 18$

$=7546 \mathrm{~cm}^{3}$

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