Question

thr diameter of a sphere is decreased by 25 percent. what percent does its curved surface area decrease?​

Answer 1

Given:

Diameter of a sphere is decreased by 25%

To Find:

The percentage decrease in the curved surface area

Explanation:

According to the property of similar figures,

$\text{Scale factor the area} = \bigg(\dfrac{\text{length1}}{\text{length2}} \bigg)^2$

Solution:

Define the diameter:

Let the diameter be x

The diameter is decreased by 25%:

25% of x = 0.25x

New diameter = x - 0.25x = 0.75x

Find the scale factor of the area:

$\text{Scale factor of the area} = \bigg(\dfrac{\text{length1}}{\text{length2}} \bigg)^2$

$\text{Scale factor of the area} = \bigg(\dfrac{\text{0.75x}}{\text{x}} \bigg)^2$

$\text{Scale factor of the area} = 0.5625$

Find the new area:

$\text{New area} = 0.5625 \times 4 \pi r^2$

$\text{New area} = 2.25 \pi r^2$

Find the percentage decrease in the area:

$\text{Percentage decrease} = \dfrac{4 \pi r^2 - 2.25 \pi r^2}{4 \pi r^2} \times 100$

$\text{Percentage decrease} =43.75\%$

Answer: The curved surface area is decreased by 43.75%

Answer 2

Answer:

43.75 percent decreased.......