Let's first determine the volume of the rectangular prism.
The rectangular prism has a length of 8 in, width of 6 in, and height of 4 in.
Volume of prism = Length x Width x Height
Volume of prism = 8 in x 6 in x 4 in
Volume of prism = 192 cubic inches
Now, the volume of a sphere can be calculated as:
Volume of sphere = (4/3) x π x radius^3
Volume of sphere = (4/3) x π x 3.7 in x 3.7 in x 3.7 in
Volume of sphere ≈ 195.13 cubic inches
Since the sphere is designed to hold as much volume as the rectangular prism, its volume should be approximately equal to 192 cubic inches. Therefore, we need to adjust the radius until we reach a volume close to 192 cubic inches.
Let's try a radius of 3.6 in:
Volume of sphere = (4/3) x π x 3.6 in x 3.6 in x 3.6 in
Volume of sphere ≈ 195.12 cubic inches
This is a close match to the volume of the prism. Now, we can calculate the surface area of the sphere:
Surface area of a sphere = 4 x π x radius^2
Surface area of sphere = 4 x π x 3.6 in x 3.6 in
Surface area of sphere ≈ 161.15 square inches
Rounded to the nearest square inch, the surface area of the sphere is 161 square inches.
A spherical container is designed to hold as much volume as the rectangular prism above. Its radius is 3.7 in. Find the surface area of the sphere rounded to the nearest square inch.(2 points) Responses
172 square inches
141 square inches
128 square inches
216 square inches
1 answer