To find the volume of the rectangular prism, we need to multiply its length, width, and height:
Volume = length x width x height = 8 in x 5 in x 7 in = 280 cubic inches
Since we want the spherical container to hold the same volume, we can set up the equation for the volume of a sphere:
Volume = (4/3)πr^3
280 = (4/3)π(3.2)^3
280 = (4/3)π(32.768)
280 = 43.274π
Solving for π, we get π ≈ 280 / 43.274 = 6.47
Now, we can calculate the surface area of the sphere using the formula:
Surface area = 4πr^2
Surface area = 4(6.47)(3.2)^2 ≈ 129 square inches
Therefore, the surface area of the sphere rounded to the nearest square inch is approximately 129 square inches. The answer is 129 square inches.
A spherical container is designed to hold as much volume as the rectangular prism above. Its radius is 3.2 in. Find the surface area of the sphere rounded to the nearest square inch. * 43 square inches 129 square inches 137 square inches 412 square inches
5 answers
Using your answers from above, which design would cost less in packaging?
*
the rectangular prism with dimensions of 8 in. x 1.5 in. x 11 in
the sphere with a radius of 3.2 in.
*
the rectangular prism with dimensions of 8 in. x 1.5 in. x 11 in
the sphere with a radius of 3.2 in.
To determine which design would cost less in packaging, we need to calculate the surface area of each shape.
For the rectangular prism with dimensions of 8 in. x 1.5 in. x 11 in:
Surface area = 2lw + 2lh + 2wh
Surface area = 2(8)(1.5) + 2(8)(11) + 2(1.5)(11)
Surface area ≈ 53 square inches
For the sphere with a radius of 3.2 in:
Surface area = 4πr^2
Surface area ≈ 4(6.47)(3.2)^2
Surface area ≈ 129 square inches
Comparing the two, the rectangular prism has a surface area of 53 square inches while the sphere has a surface area of 129 square inches. This means that the rectangular prism would cost less in packaging as it has a smaller surface area.
For the rectangular prism with dimensions of 8 in. x 1.5 in. x 11 in:
Surface area = 2lw + 2lh + 2wh
Surface area = 2(8)(1.5) + 2(8)(11) + 2(1.5)(11)
Surface area ≈ 53 square inches
For the sphere with a radius of 3.2 in:
Surface area = 4πr^2
Surface area ≈ 4(6.47)(3.2)^2
Surface area ≈ 129 square inches
Comparing the two, the rectangular prism has a surface area of 53 square inches while the sphere has a surface area of 129 square inches. This means that the rectangular prism would cost less in packaging as it has a smaller surface area.
Using your answers from above, which design would cost less in packaging?
*
A.the rectangular prism with dimensions of 8 in. x 1.5 in. x 11 in
B.the sphere with a radius of 3.2 in.
*
A.the rectangular prism with dimensions of 8 in. x 1.5 in. x 11 in
B.the sphere with a radius of 3.2 in.
When comparing the packaging costs based on the surface areas calculated earlier:
A. The rectangular prism with dimensions of 8 in. x 1.5 in. x 11 in has a surface area of 53 square inches.
B. The sphere with a radius of 3.2 in has a surface area of 129 square inches.
Since the rectangular prism has a smaller surface area (53 square inches) compared to the sphere (129 square inches), the rectangular prism would cost less in packaging.
Therefore, the design of the rectangular prism with dimensions of 8 in. x 1.5 in. x 11 in would cost less in packaging compared to the sphere with a radius of 3.2 in.
A. The rectangular prism with dimensions of 8 in. x 1.5 in. x 11 in has a surface area of 53 square inches.
B. The sphere with a radius of 3.2 in has a surface area of 129 square inches.
Since the rectangular prism has a smaller surface area (53 square inches) compared to the sphere (129 square inches), the rectangular prism would cost less in packaging.
Therefore, the design of the rectangular prism with dimensions of 8 in. x 1.5 in. x 11 in would cost less in packaging compared to the sphere with a radius of 3.2 in.
1 answer