Question

david and karen are building a tree house in the shape of a rectangular prism for their daughter. if the tree house is going to 5 feet tall, 8 feet tall, 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 inside the tree is 300 cubic feet

David have to paint 275 square feet on the outside

Solution:

The tree house is going to 5 feet tall, 8 feet wide, and 7.5 feet long

Length = 7.5 feet

Width = 8 feet

Height = 5 feet

The tree house in the shape of a rectangular prism

The volume of rectangular prism is given as:

$Volume = length \times width \times height$

Substituting the values we get,

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

Thus space inside the tree is 300 cubic feet

How much space will they have to paint on the outside?

We have to find the surface area of prism

The surface area of prism is given as:

$A=2(wl+hl+hw)$

Substituting the values we get,

$A = 2((8 \times 7.5) + (5 \times 7.5) + (5 \times 8))\\\\A = 2(60+37.5+40)\\\\A = 2 \times 137.5\\\\A = 275$

Thus they have paint 275 square feet on the outside