Question

3. The radii of the internal and external surfaces of
a metallic spherical shell are 3 cm and 5 cm
respectively. It is melted and recast into a solid
right circular cone of height 32 cm. Find the
diameter of the base of the cone.​

Answer 1

Step-by-step explanation:

vol³ of the metallic sphere= ext. vol³- int. vol³

= (4/3)π5³-(4/3)π3³

= (4/3)π(125-27)

= (4/3)π× 98cm³

now vol³of a cone = vol³ of sphere

πr²(h/3) = (4/3)π × 98cm³

(32cm)r²= 4×98cm³

(8cm)r²= 98cm³

r²= 98cm³/8cm

r= √12.25cm²= 3.5cm