Question

The radius and the height of a cone are in
the ratio 7:3. If the volume of a cone is
9856 cm3, then the height of the cone is
एक शंकु की त्रिज्या व ऊँचाई का अनुपात 7:3 है। यदि
शंकु का आयतन 9856 cm3 है, तब शंकु की ऊँचाई है​

Answer 1

Given,

The ratio of height and radius of the cone = 7:3

The volume of the cone = 9856 cm cube

To Find,

The height of the cone.

Solution,

Let the height and radius of the cone be 7x and 3x.

Now,

Volume = 1/3 πr²h

9856 = 1/3 × 22/7 × (7x)² × 3x

9856 = 1/3 × 22/7 × 49x² × 3x

9856 = 22 × 7x³

9856 = 154x³

9856 = 154x³

x³ = 64

x = 4

So, the value of height would be 3x = 3(4) = 12.

Hence, the value of height of the cone is 12 cm.

Answer 2

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex.

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

Now, according to quetion,

Let the radius and height of a cone be $x.$

So Radius $=7x$

Height $=3x$

Volume of cone $=\frac{1}{3}\pi r^2h$

$9856=\frac{1}{3}\times \frac{22}{7}\times 7x\times 7x\times 3x$

$\frac{9856}{22\times 7}=x^3$

$x^3=64\\x=4$

So, the height of the cone is

$3x=3\times4=12cm$