Question

I NEED HELP ASAP I WILL GIVE 100 PTS IF YOU HELP ME AND GIVE RIGHT ANSWER AND I NEED EXPLANATION PLS HELP

A student is painting a doghouse like the rectangular prism shown.

A rectangular prism with base dimensions of 8 feet by 6 feet. It has a height of 5 feet.

Part A: Find the total surface area of the doghouse. Show your work. (3 points)

Part B: If one can of paint will cover 50 square feet, how many cans of paint are needed to paint the doghouse? Explain. (Hint: The bottom will not be painted since it will be on the ground.) (1 point)

Answer 1

A) 236 ft²

B) 4 cans of paint

Explanation:

Part A

The given diagram (attached) shows the doghouse modelled as a rectangular prism with the following dimensions:

• width = 6 ft
• length = 8 ft
• height = 5 ft

The formula for the total surface area of a rectangular prism is:

`S.A.=2(wl+hl+hw)`

where w is the width, l is the length, and h is the height.

To find the total surface area of the doghouse, substitute the given values of w, l and h into the formula:

`\begin{aligned}\textsf{Total\;surface\;area}&=2(6 \cdot 8+5 \cdot 8+5 \cdot 6)\\&=2(48+40+30)\\&=2(118)\\&=236\; \sf ft^2\end{aligned}`

Therefore, the total surface area of the doghouse is 236 ft².

`\hrulefill`

Part B

As the bottom of the doghouse will not be painted, to find the total surface area to be painted, subtract the area of the base from the total surface area:

`\begin{aligned}\textsf{Area\;to\;be\;painted}&=\sf Total\;surface\;area-Area\;of\;base\\&=236-(8 \cdot 6)\\&=236-48\\&=188\; \sf ft^2\end{aligned}`

Therefore, the total surface area to be painted is 188 ft².

If one can of paint will cover 50 ft², to calculate how many cans of paint are needed to paint the doghouse, divide the total surface area to be painted by 50 ft², and round up to the nearest whole number:

`\begin{aligned}\textsf{Cans\;of\;paint\;needed}&=\sf (188\;ft^2)/(50\;ft^2)\\\\ &= \sf 3.76\\\\&=\sf 4\;(nearest\;whole\;number)\end{aligned}`

Therefore, 4 cans of paint are needed to paint the doghouse.

Note: Rounding 3.76 to the nearest whole number means rounding up to 4. However, even if the number of paint cans needed was nearer to 3, e.g. 3.2, we would still need to round up to 4 cans, else we would not have enough paint.

Answer 2

A: 236 sqaure ft.

B: 4 cans

Explanation:

Sure, I can help you with that.

Part A:

The total surface area of a rectangular prism is calculated using the following formula:

Total surface area = 2(lw + wh + lh)

where:

• l = length
• w = width
• h = height

In this case, we have:

• l = 8 feet
• w = 6 feet
• h = 5 feet

Plugging these values into the formula, we get:

Total surface area = 2(8*6+6*5+8*5) = 236 square feet

Therefore, the total surface area of the doghouse is 236 square feet.

Part B:

Since the bottom of the doghouse will not be painted, we only need to paint the top, front, back, and two sides.

The total surface area of these sides is 236-6*8 = 188 square feet.

Therefore,

we need 188 ÷ 50 = 3.76 cans of paint to paint the doghouse.

Since we cannot buy 0.76 of a can of paint, we need to buy 4 cans of paint.