Question

This question has three parts. A playground has two sandboxes Each sandbox is shape of a prism Part A The first sandbox has a square base with a side length of feet What is the area in square , of the base of the first sandbox? Show or explain how you got your answer Enter your answer and your work or explanation in the space provided Part B The groundskeeper filled the first sandbox with sand to a height of 6 inchesWhat is the volume, in cubic feet of the sand that was used to fill the first sandbox to a height of 6 inches? Show or explain how you got your answer Part CAfter filling the first sandbox to a height of 6 inches, the groundskeeper had 24 cubic feet of sand left over She used the leftover sand to fill the second sandbox The second sandbox has a base in the shape of a rectangle The base of the second sandbox has a perimeter that is less than 35 feet The groundskeeper filled the second sandbox to a height of 6 inches. What could be the length and widthin feet , of the second sandbox ? Show or explain how you got your answers

Answer 1

The Sandbox is a shape of a prism

Part A

The Lenght of the base is 8 feet

the area of the base is

$\begin{gathered} l^2 \\ 8^2=8\times8=64ft^2 \end{gathered}$

The area of the base 64 square feet

The area of the base is the area of a square in which all the side are equal

Part B

The first sandbox is a squared based prism

The volume of a prism is given by

$\text{Base area x height}$

The base area=64 square feet and the height=6 inches

convert inches to feet

1 inches = 0.0833 foot

6 inches=6 x 0.0833=0.4998feet

Hence the volume of the sand in the sandbox is

$\begin{gathered} 64\times0.4998 \\ 31.9872\text{cubic f}eet \end{gathered}$

Therefore the volume of sand used to fill the sandbox is 31.9872 cubic feet

Part C

The volume of sand left=24cubic feet

The second sandbox is a rectangular base prism

The perimeter is less than 35feet

The volume of the second sandbox fill to height 6 inches is 24 cubic feet

hence we need to find the area of the base

$\begin{gathered} \text{volume}=\text{base area}\times height \\ 24=\text{base area}\times0.4998 \\ \text{base area=}\frac{24}{0.4998} \\ 48.02\text{ f}eet \\ \text{since 6inches=0.4998f}eet \end{gathered}$

The perimeter is less than 35

the perimeter of a rectangle is 2(L+B)

2(L+B)<35