Question

A solid cone of radius 5cm and heigt 8 cm is melted and made into small spheres of radius 0.5cm.Find the number of spheres formed?​

Answer 1

Answer:

400 spheres

Step-by-step explanation:

First you need to find the volume of the cone, the equation is:

V = $\frac{1}{3}\pi r^{2}h$ -  so the volume is:

V = (25π × 8) ÷ 3

V = (200π ÷3)

Then we need to find the volume of the spheres, the equation is:

$V=\frac{4}{3} \pi r^{3}$ -  so the volume is:

V = (0.5π ÷ 3)

Then we divide the volume of the cone by the volume of the sphere and we get how many spheres we can form:

(200π ÷ 3) ÷ (0.5π ÷ 3) = 400

Answer 2

Answer:

for the cone ,

radius of cone, r1 = 5cm

height of the cone, h = 8cm

for the spheres ,

radius of the sphere, r2 = 0.5cm

No. of spheres formed from melted cone

= volume of the cone

volume of the sphere

= 1/ 3 π (r1)^2 h = (r1)^2 × h

4/ 3 π (r2)^3 4 × (r2)3

= 5× 5 × 8 = 25 × 2

4× (0.5)^3. 0.125

= 25 × 2 × 1000. = 2000 = 400

125. 5

Therefore, 400 spheres are formed.