Question

What is the surface area of the box, in square meters, that Chase decorates?

13 m, 9 m, 9 m, 6 m, 10.82 m, 10.82 m

Answer 1

What is the surface area of the cylinder with height 7 m and radius 8 m? Round your answer to the nearest thousandth.

Answer 2

To find the surface area of the box, we need to calculate the area of each of the six sides and then add them all together.

Side 1: 13m x 9m = 117 sq meters
Side 2: 13m x 9m = 117 sq meters
Side 3: 9m x 6m = 54 sq meters
Side 4: 9m x 6m = 54 sq meters
Side 5: 10.82m x 6m = 64.92 sq meters
Side 6: 10.82m x 6m = 64.92 sq meters

Total surface area = 117 + 117 + 54 + 54 + 64.92 + 64.92 = 472.84 sq meters

Therefore, the surface area of the box that Chase decorates is 472.84 square meters.

Answer 3

To find the surface area of a cylinder, we need to calculate the areas of the two circular bases and the lateral surface area (the curved surface area).

The formula for the lateral surface area of a cylinder is:
Lateral Surface Area = 2 x π x r x h, where r is the radius and h is the height.

Given:
Radius (r) = 8m
Height (h) = 7m

Lateral Surface Area = 2 x π x 8 x 7
Lateral Surface Area = 2 x 3.14159 x 8 x 7
Lateral Surface Area = 351.85824 sq meters

The formula for the area of a circle (base of the cylinder) is:
Base Area = π x r^2

Base Area = 3.14159 x 8^2
Base Area = 3.14159 x 64
Base Area = 200.96022 sq meters

Total Surface Area = Lateral Surface Area + 2 x Base Area
Total Surface Area = 351.85824 + 2 x 200.96022
Total Surface Area = 351.85824 + 401.92044
Total Surface Area = 753.77868 sq meters

Therefore, the surface area of the cylinder with a height of 7m and a radius of 8m is approximately 753.779 square meters.