Question

What's the percentage change in the curved surface area of a hemisphere if the radius is doubled the initial radius?

A. 100 %

B. 300 %

C. 50 %

D. 150 %

Answer 1

The percentage change in the curved surface area of a hemisphere when the radius is doubled is 300%.

Step-by-step explanation:

To find the percentage change in the curved surface area of a hemisphere when the radius is doubled, we need to compare the curved surface area of the hemisphere with the initial radius to the curved surface area of the hemisphere with the doubled radius.

The curved surface area of a hemisphere is given by the formula: CSA = 2πr², where r is the radius.

If we double the radius, the new curved surface area of the hemisphere would be: CSA' = 2π(2r)² = 8πr².

To find the percentage change, we can use the formula: Percentage Change = ((CSA' - CSA)/CSA) * 100%.

Substituting the values, we have: ((8πr² - 2πr²)/2πr²) * 100% = ((6πr²)/2πr²) * 100% = 300%.

Therefore, the percentage change in the curved surface area of the hemisphere when the radius is doubled is 300%.