Question

Two spheres have volumes of 8pi cm cubed and 64pi cm cubed. If the surface area of the smaller sphere is 16pi cm squared, what is the surface area of the larger sphere.

Answer 1

The surface area of the larger sphere is calculated to be 32pi cm^2, using the given volumes of two spheres and the surface area of the smaller sphere along with the sphere volume and surface area formulas.

Step-by-step explanation:

To find the surface area of the larger sphere using the given volumes of two spheres and the surface area of the smaller sphere, we use the formulas for the volume V = 4/3 (pi) (r)^3 and surface area SA = 4 (pi) (r)^2.

Firstly, we calculate the radius of the smaller sphere whose volume is 8pi cm^3:

• V_small_sphere = 4/3 (pi) (r_small)^3
• 8pi = 4/3 pi (r_small)^3
• 2 = (r_small)^3
• r_small = cuberoot(2)

Given that the surface area of the smaller sphere is 16pi cm^2, we can find its exact radius:

• SA_small_sphere = 4 pi (r_small)^2
• 16pi = 4pi (r_small)^2
• 4 = (r_small)^2
• r_small = 2

Now, we calculate the larger sphere’s radius using its volume of 64pi cm^3:

• V_large_sphere = 4/3 pi (r_large)^3
• 64pi = 4/3 pi (r_large)^3
• 48/3 = (r_large)^3
• r_large = cuberoot(16)
• r_large = 2*cuberoot(2)

Finally, we can use the radius to calculate the surface area of the larger sphere:

• SA_large_sphere = 4 pi (r_large)^2
• SA_large_sphere = 4 pi (2*cuberoot(2))^2
• SA_large_sphere = 4 pi (4 * 2)
• SA_large_sphere = 32pi cm^2

Hence, the surface area of the larger sphere is 32pi cm^2.