Question

Q. 4. A metallic cylinder of radius 8 cm and height 6 cm is melted and converted into a right circular cone of height 6 cm. Find the radius of the base of the cone.​

Answer 1

Answer:

volume of cylinder = πr^2h = volume of cone =1/3πr'^2h'

thus , πr^2h = 1/3πr'^2h'

r^2h = 1/3r'^2 h'

8^2×6 = 1/3×r'^2×6

r'^2 = 64×3

r' = 13.86 cm answer.

Answer 2

Answer:

• 13.86 cm

Step-by-step explanation:

Given

• Radius of cylinder = 8 cm
• Height of cylinder = 6 cm
• Height of cone = 6 cm

A metallic cylinder is melted and converted to a right circular cone.

To find

• Radius of cone

Solution

According to the question, a metallic cylinder is melted and converted into a right circular cone, so that means both their volumes will be equal and we are given with dimensions of cylinder and only the height of cone and are asked to find the radius of cone, so if we simply equate the volumes we can find the radius of cone.

Volume of cylinder = πr²h

Volume of cone = ⅓πr²h

• ²²⁄₇ × 8 × 8 × 6 = ⅓ × ²²⁄₇ × r² × 6
• 8 × 8 × 6 = 2 × r²
• 384 = 2r²
• r² = 192
• r = 13.856406

Hence, the radius of cone is 13.86 cm.