Name: Mensuration Formulas
Uploaded: 2019-07-19
Duration: 10 min 20 s
Description: Various mensuration formula is covered in geometry useful for the exam point. In order to excel in this topic, you must know the formulas and concepts used t...

Question

A solid is in the shape of frustum of a cone. The diameters of the two circular ends are

60 cm

and

36 cm

and the height is

9 cm

. Find the area of its whole surface and the volume.

Accepted Answer

Given diameter of the top circular end of the frustum of a cone $= 60 cm$

Radius of the top of the frustum of a cone $(R) = 30 cm$

Given diameter of the bottom circular end of the frustum of a cone $= 36 cm$

Radius of the bottom of the frustum of a cone $= 18 cm$

Height of the frustum of a cone $= 9 cm$

Slant height of the frustum of a cone $l = \sqrt{h^{2} + {(R - r)}^{2}}$

Slant height of the frustum of a cone $l = \sqrt{9^{2} + {(30 - 18)}^{2}} = \sqrt{81 + 144} = \sqrt{225} = 15 cm$

We know that the total surface area of a cone $= π (r + R) l + π r^{2} + π R^{2}$

We know that the curved surface area of the frustum of a cone $= π (r + R) l$

Curved surface area of the frustum of a cone $= π (30 + 18) \times 15 = π (48 \times 15) {cm}^{2}$

Total surface area of the frustum of a cone $=$ Curved surface area of the frustum of a cone $+$ Area of the bottom circular end $+$ Area of the top circular end

Area of the bottom circular end $= π r^{2}$ $= π \times 324 {cm}^{2}$

Area of the top circular end $= π R^{2} = π \times 900$

Total surface area of the frustum of a right circular cone $= π [720 + 900 + 324] = 1944 π {cm}^{2}$

We know that the Volume of a frustum of a right circular cone $= \frac{1}{3} π h (r^{2} + r R + R^{2})$

Volume $= \frac{1}{3} \times π \times 9 (30^{2} + 18^{2} + 30 \times 18) = \frac{1}{3} \times π \times 9 \times 9 (100 + 36 + 60) {cm}^{3}$

Volume $= 27 π \times 196 = 5292 π {cm}^{3}$

Hence, the Volume of frustum of a cone is $5292 π {cm}^{3}$

A solid is in the shape of frustum of a cone. The diameters of the two circular ends are $60 cm$ and $36 cm$ and the height is $9 cm$ . Find the area of its whole surface and the volume.

Important Questions on Surface Areas and Volumes

Learn and Prepare for any exam you want !

A solid is in the shape of frustum of a cone. The diameters of the two circular ends are 60 cm and 36 cm and the height is 9 cm. Find the area of its whole surface and the volume.

Important Questions on Surface Areas and Volumes

Learn and Prepare for any exam you want !

A solid is in the shape of frustum of a cone. The diameters of the two circular ends are $60 cm$ and $36 cm$ and the height is $9 cm$ . Find the area of its whole surface and the volume.