Question

the sphere has the same curved surface of a cone of height 12 cm and base radius 5 cm. find the radius of nearest cm

Answer 1

Answer:

Step-by-step explanation: h = 12 cm

r = 5 cm

l = √h²+r² = √144+25 = √169 = 13 cm

let the radius if the sphere be 'R' cm.

∴ As per the sum ,

                4πR² = πrl

                 4 × R² = 5 × 13

                       R² = 65/4

                       R  = √65/2

                           = 8.06/2

                           = 4.06 cm

             therefore , radius of nearest cm = 4 cm .

Answer 2

Given:-

• A sphere has some curved surface as a cone.
• Height and base Radius of cone is 12cm and 5cm.

To find:-

• Find the radius of nearest cm...?

Solutions:-

• Let the radius of the sphere be r cm.

The curved surface area of sphere is equal to the curved surface area of a cone.

CSA of sphere = CSA of cone

The slant height of the cone => l² = h² + r²

=> l² = (12)² + (5)²

=> l² = 144 + 25

=> l² = 169

=> l = √169

=> l = 13

Now,

CSA of sphere = CSA of cone

=> 4πr² = πrl

=> 4 × π × r² = π × 12 × 5

=> 4 × r² = 12 × 5

=> r² = 12 × 5/4

=> r² = 3 × 5

=> r² = 15

=> r = √15

=> r = 3.87cm.

Hence, the radius of the sphere is 3.87 cm.