Name: Volume of Frustum of a Cone
Uploaded: 2019-07-19
Duration: 5 min 12 s
Description: In geometry, a frustum is the portion of a solid, normally a cone that lies between one or two parallel planes cutting it. Learn how to find the volume of th...

Question

A metal cup is in the form of a frustum of a cone whose radii of bottom and top are $7 c m$ and $14 c m$ respectively, as shown in the figure. If the capacity of the cup is $2156 {cm}^{3}$ , find the height of the cup. $(Use π = \frac{22}{7})$

Accepted Answer

Given, volume of the metal cup which is in the form of a frustum of a cone is $2156 {cm}^{3}$ .

We need to find the height of the metal cup.

Let $r_{1} = 7 c m$ , and $r_{2} = 14 c m$

We know that

Volume of the metal cup in the form of a frustum of a cone $= \frac{1}{3} π h (r_{1}^{2} + r_{2}^{2} + r_{1} r_{2})$

$\Rightarrow 2156 = \frac{1}{3} \times \frac{22}{7} \times h (7^{2} + 14^{2} + 7 \times 14)$

$\Rightarrow 2156 = \frac{1}{3} \times \frac{22}{7} \times h (49 + 196 + 98)$

$14 c m$

$\Rightarrow 343 h = \frac{2156 \times 21}{22}$

$\Rightarrow h = \frac{2156 \times 21}{22 \times 343}$

Hence, the required height is $6 c m$

A metal cup is in the form of a frustum of a cone whose radii of bottom and top are $7 c m$ and $14 c m$ respectively, as shown in the figure. If the capacity of the cup is $2156 {cm}^{3}$ , find the height of the cup. $(Use π = \frac{22}{7})$

Important Questions on Surface Areas and Volumes

Learn and Prepare for any exam you want !

A metal cup is in the form of a frustum of a cone whose radii of bottom and top are 7 cm and 14 cm respectively, as shown in the figure. If the capacity of the cup is 2156 cm3 , find the height of the cup. (Use π=227 )

Important Questions on Surface Areas and Volumes

Learn and Prepare for any exam you want !

A metal cup is in the form of a frustum of a cone whose radii of bottom and top are $7 c m$ and $14 c m$ respectively, as shown in the figure. If the capacity of the cup is $2156 {cm}^{3}$ , find the height of the cup. $(Use π = \frac{22}{7})$