Question

David and Karen are building a treehouse in the shape of a rectangular prism for their daughter.If the treehouse is going to 5 feet tall 8 feet wide and 7.5 feet long How much space will there be inside? How much space will they have to paint on the outside?

Answer 1

The space left inside the tree is 300 cubic feet.

David and Karen have to paint 275 square feet on the outside.

Explanation:

It is given that the length of the tree house is 7.5 feet

The width of the tree house is 8 feet

The height of the tree house is 5 feet

The tree house is in the shape of a rectangular prism.

The volume of the rectangular prism is given by

$\text {Volume}=\text {length } \times \text {width} \times \text {height}$

Substituting the values, we have,

$Volume =7.5 \times 8 \times 5 \\Volume =300$

Thus, the volume of the rectangular prism is 300 cubic feet

Hence, the space left inside the tree is 300 cubic feet.

The area they have to paint on the outside can be determined using the formula for surface area of the prism .

$Area=2(w l+h l+h w)$

Substituting the values, we get,

$Area=2[(8*7.5)+(5*7.5)+(5*8)]$

Multiplying the terms within the bracket, we get,

$Area=2(60+37.5+40)$

Adding the terms, we have,

$Area=2 \times 137.5$

Multiplying, we get,

$Area =275$

Thus, David and Karen have to paint 275 square feet on the outside.