The formula for the surface area of a sphere is 4πr2. Sphere A has a radius of 3 cm and sphere B has a radius of 6 cm. Calculate the surface area of each sphere and compare their surface areas. (2 points)

Question

Sphere A has a surface area of ____π cm2. Sphere B has a surface area of ____π cm2. The surface area of sphere B is ____
times larger than the surface area of sphere A.

Answer 1

To calculate the surface area of each sphere, we can use the formula for the surface area of a sphere, which is \(4\pi r^2\).

For Sphere A:

• Radius \(r = 3\) cm
• Surface Area = \(4\pi(3^2)\)
• Surface Area = \(4\pi(9)\)
• Surface Area = \(36\pi\) cm²

For Sphere B:

• Radius \(r = 6\) cm
• Surface Area = \(4\pi(6^2)\)
• Surface Area = \(4\pi(36)\)
• Surface Area = \(144\pi\) cm²

Comparison:

Now, we need to compare their surface areas:

• Sphere A has a surface area of \(36\pi\) cm².
• Sphere B has a surface area of \(144\pi\) cm².

To find how many times larger the surface area of Sphere B is compared to Sphere A, we can divide the surface area of Sphere B by the surface area of Sphere A:

\[ \text{Ratio} = \frac{144\pi}{36\pi} = \frac{144}{36} = 4 \]

Final Answers:

• Sphere A has a surface area of 36π cm².
• Sphere B has a surface area of 144π cm².
• The surface area of sphere B is 4 times larger than the surface area of sphere A.