Maths-

General

Easy

Question

# A cone has slanted height of 5cm and height of 4cm, its volume (in cm^{3} ) is

__________

- 38.71
- 36.50
- 37.00
- 37.68

Hint:

### Volume of a cone = (1/3)πr2h

By applying Pythagoras theorem on the cone, we can find the relation between volume and slant height of the cone.

We know, h2 + r2 = L2

where,

h is the height of the cone,

r is the radius of the base, and,

L is the slant height of the cone.

The volume of the cone in terms of slant height can be given as

V = (1/3)πr2h =

## The correct answer is: 37.68

### We have given that

Slanted height L = 5 cm

Height, h = 4cm

From these given values we can find the radius of base of cone

We know that

h^{2} + r^{2} = L^{2}

r^{2} = L^{2} - h^{2}

= 5^{2 }– 4^{2}

= 25 – 16

r^{2} = 9

r= 3

So, the volume of cone = ()πr^{2}h

= ()(3.14)(3 x 3)(4)

= 3.14 x 3 x 4

= 37.68

Therefore, the correct option is d) 37.6

^{2}+ r

^{2}= L

^{2}

^{2}= L

^{2}- h

^{2}

^{2 }– 4

^{2}

^{2}= 9

So, the volume of cone = ()πr

^{2}h

Therefore, the correct option is d) 37.6

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