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 frustum of a right circular cone has a diameter of base

20 cm

, of top

12 cm

and height

3 cm

. Find the area of its whole surface and volume.

Accepted Answer

Given diameter of the top circular end of the frustum of a cone $= 20 cm$

Radius of the top of the frustum of a cone $(R) = 10 cm$

Given diameter of the bottom circular end of the frustum of a cone $= 12 cm$

Radius of the bottom of the frustum of a cone $= 6 cm$

Depth of the frustum of a cone $= 3 cm$

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

Slant height of the frustum of a cone $l = \sqrt{3^{2} + {(10 - 6)}^{2}} = \sqrt{25} = 5 cm$

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 $= \frac{22}{7} (10 + 6) \times 5 {cm}^{2}$

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 $= π r^{2}$ $= \frac{22}{7} \times 36 {cm}^{2}$

Area of the top circular end $= π R^{2} = \frac{22}{7} \times 100$

Total surface area of the frustum of a right circular cone $= \frac{22}{7} (16) \times 5 + \frac{22}{7} \times 36 + \frac{22}{7} \times 100$

Total surface area $= \frac{22}{7} [80 + 36 + 100] = \frac{22}{7} \times 216 = 678.85 {cm}^{2}$

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 $= \frac{1}{3} \times \frac{22}{7} \times 3 (100 + 60 + 36) = \frac{22}{7} \times 196 = 616 {cm}^{3}$

Hence, the Volume of frustum of a cone is $616 {cm}^{3}$

Note: The answer given in the back of book is wrong and the correct answer is mentioned as above.

A frustum of a right circular cone has a diameter of base $20 cm$ , of top $12 cm$ and height $3 cm$ . Find the area of its whole surface and volume.

Important Questions on Surface Areas and Volumes

Learn and Prepare for any exam you want !

A frustum of a right circular cone has a diameter of base 20 cm, of top 12 cm and height 3 cm. Find the area of its whole surface and volume.

Important Questions on Surface Areas and Volumes

Learn and Prepare for any exam you want !

A frustum of a right circular cone has a diameter of base $20 cm$ , of top $12 cm$ and height $3 cm$ . Find the area of its whole surface and volume.