Question

a solid metallic right circular cylinder 1.8 m high with demographics base 2 metre is melted and recast into a right circular cone with base of diameter 3 M find the height of the cone

Answer 1

the height of the cone is 2.4m.

Answer 2

Answer:

2.4 m

Step-by-step explanation:

Given : Height of cylinder = 1.8 m

          Diameter of cylinder = 2 m

          Diameter of cone = 3 m

To Find: height of the cone

Solution :

Diameter of cylinder = 2 m

Radius = diameter/2 = 2/2 = 1 m

Volume of cylinder = $\pi r^{2} h$

                                 = $\pi 1^{2} \times 1.8$

Diameter of cone = 3 m

Radius of cone = diameter/2 = 3/2 =1.5

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

                           = $\frac{1}{3} \pi 1.5^{2}\times h$

Since the cylinder is recast into cone by melting it .So volume will remain same

$\pi 1^{2} \times 1.8= \frac{1}{3} \pi 1.5^{2} h$

$1.8= \frac{1}{3}\times 2.25\times h$

$1.8\times 3= 2.25\times h$

$5.4= 2.25\times h$

$\frac{5.4}{2.25}=h$

$2.4=h$

Hence the height of cone is 2.4 m