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
(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:
$=1 / 3 \pi r^{2} h$
$=\frac{1}{3} * 3.14 *(7 \sqrt{7})^{2} * 18$
$=7546 \mathrm{~cm}^{3}$