Question

(Please help!!!) A landscaper is creating a bench for a pool deck. A model of the bench is shown in the image.

A rectangular prism with dimensions of 6.2 feet by 3 feet by 4 feet.

Part A: Find the total surface area of the bench. Show all work. (6 points)

Part B: The landscaper will cover the bench in ceramic tiles except for the bottom that is on the ground. If the tiles cost $0.83 per square foot, how much will it cost to cover the bench? Show all work. (6 points)

Answer 1

$76.526

Explanation:

Front and back: length = 6.2 feet, width = 4 feet

Left and right: length = 3 feet, width = 4 feet

Top and bottom: length = 6.2 feet, width = 3 feet

The area of each face is:

Front and back: A = lw = (6.2)(4) = 24.8 square feet

Left and right: A = lw = (3)(4) = 12 square feet

Top and bottom: A = lw = (6.2)(3) = 18.6 square feet

The total surface area is the sum of the areas of all six faces:

SA = 2(24.8) + 2(12) + 2(18.6) SA = 49.6 + 24 + 37.2 SA = 110.8 square feet

Part B: To find the cost of covering the bench in ceramic tiles, we need to find the surface area of the bench excluding the bottom face that is on the ground. This is the same as the total surface area minus the area of the bottom face:

SA’ = SA - A(bottom) SA’ = 110.8 - 18.6 SA’ = 92.2 square feet

The cost of covering one square foot of the bench is $0.83, so the total cost is:

C = SA’ x $0.83 C = 92.2 x $0.83 C = $76.526

Rounding to the nearest cent, the cost is $76.53.

Received message. Part A: To find the total surface area of the bench, we need to find the area of each face of the rectangular prism and add them up. The formula for the area of a rectangle is A = lw, where l is the length and w is the width. The dimensions of the bench are 6.2 feet by 3 feet by 4 feet, so we can label the faces as follows: - Front and back: length = 6.2 feet, width = 4 feet - Left and right: length = 3 feet, width = 4 feet - Top and bottom: length = 6.2 feet, width = 3 feet The area of each face is: - Front and back: A = lw = (6.2)(4) = 24.8 square feet - Left and right: A = lw = (3)(4) = 12 square feet - Top and bottom: A = lw = (6.2)(3) = 18.6 square feet The total surface area is the sum of the areas of all six faces: SA = 2(24.8) + 2(12) + 2(18.6) SA = 49.6 + 24 + 37.2 SA = 110.8 square feet Part B: To find the cost of covering the bench in ceramic tiles, we need to find the surface area of the bench excluding the bottom face that is on the ground. This is the same as the total surface area minus the area of the bottom face: SA' = SA - A(bottom) SA' = 110.8 - 18.6 SA' = 92.2 square feet The cost of covering one square foot of the bench is $0.83, so the total cost is: C = SA' x $0.83 C = 92.2 x $0.83 C = $76.526 Rounding to the nearest cent, the cost is $76.53.

Answer 2

The answer to your problem is ↓

Part A: 110.8 feet

Part B: $77

Explanation:

Calculation: Part A.

6.2 x 4 = 24.8

24.8 x 2 = 49.6

4 x 3 = 12

12 x 2 = 24

6.2 x 3 = 18.6

18.6 x 2 = 37.2

49.6 + 24 + 37.2 = 110.8

Calculation: Part B.

Same as the beginning of Part A:

6.2 x 4 = 24.8

24.8 x 2 = 49.6

4 x 3 = 12

12 x 2 = 24

6.2 x 3 = 18.6

49.6 + 24 + 18.6 = 92.2

92.2 x .83 = 76.526

We then need to round ‘ 76.526 ‘

Rounded = 77

Thus the answer to your problem is ↓

Part A: 110.8 feet

Part B: $77