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
[tex]\text {Volume}=\text {length } \times \text {width} \times \text {height}[/tex]
Substituting the values, we have,
[tex]Volume$=7.5 \times 8 \times 5$\\Volume $=300$[/tex]
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 .
[tex]Area=2(w l+h l+h w)[/tex]
Substituting the values, we get,
[tex]Area=2[(8*7.5)+(5*7.5)+(5*8)][/tex]
Multiplying the terms within the bracket, we get,
[tex]Area=2(60+37.5+40)[/tex]
Adding the terms, we have,
[tex]Area=2 \times 137.5[/tex]
Multiplying, we get,
[tex]Area =275[/tex]
Thus, David and Karen have to paint 275 square feet on the outside.
V= L x W x H
Leight x with x height = V
5 x 8 x 7.5= V
=300feet2
Step-by-step explanation:
Hope it helps
