Question

9. A metallic sphere of diameter 42 cm is melted and recast into cones of radius 3.5 cm and height 4 cm. The number of such cones formed is​

Answer 1

Answer:

This is the question from Mensuration chapters Spheres and cones .

Step-by-step explanation:

Diameter of metallic sphere =42 cm then

Radius of metallic sphere = 21 cm

we melted it into x number of cones with radius 3.5 cm and height 4 cm ,

volume of x coins = volume of metallic sphere

$x \times \pi \times {r \:}^{2} \: \times \frac{h}{3} = \frac{4}{3} \times \pi \times {r}^{3}$

pi is cancel out both side ,

$x \: \times {3.5}^{2} \times \frac{4}{3} \: = \: \frac{4}{3} \times \: {21}^{3}$

$\frac{4}{3}$

cancel out both side and square of 3.5 is equal to 12.25 and cube of 21 is 9261

$x \: \times 12.25 = \: 9261 \\ x = \frac{9261}{12.25 } \\ x = \: 756$