Question

A sphere has same curved surface as acone of
height 360 cm and base raidus is 150 cm .find its
raidus to the nearest centimeter.​

Answer 1

GIVEN:

• A sphere has same curved surface as a cone.
• Height and base radius of cone is 360 cm and 150 cm respectively.

TO FIND:

• What is the radius of sphere ?

SOLUTION:

Let the radius of the sphere be 'r' cm

✒ We have given that, the curved surface area of sphere is equal to the curved surface area of a cone.

To find the radius of sphere we use the formula:-

❰ CSA of sphere = CSA of cone ❱

❰ 4πr² = πrl ❱

According to question:-

First, we need to find the slant height (l) of the cone:-

❮ l² = h² + r² ❯

➾ l² = (360)² + (150)²

➾ l² = 129600 + 22500

➾ l² = 152100

➾ l = $\sf{\sqrt{152100}}$

➾ l = 390 cm

Now, put the values in the formula:-

➾ 4 $\times$ π $\times$ r² = π $\times$ 150 $\times$ 390

➾ r² = $\sf{\dfrac{150 \times 390}{4}}$

➾ r² = 75 $\times$ 185

➾ r² = 13875

➾ r = $\sf{\sqrt{13875}}$

❛ radius = 117.79 cm² ❜

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