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?

Respuesta :

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:

[tex]Volume = length \times width \times height[/tex]

Substituting the values we get,

[tex]Volume = 7.5 \times 8 \times 5\\\\Volume = 300[/tex]

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:

[tex]A=2(wl+hl+hw)[/tex]

Substituting the values we get,

[tex]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[/tex]

Thus they have paint 275 square feet on the outside

The space that will be inside is 300 ft³

The space that they will have to paint on the outside is 275 ft²

The tree house is in the shape of a rectangular prism. The dimension of the prism is as follows:

length = 7.5 ft

width = 5 ft

height = 8 ft

The number of space inside is the volume of the rectangular prism. Therefore,

volume = lwh

volume  = 7.5 × 5 × 8 = 300 ft³

The space they will paint outside is the total surface area of the rectangular prism. Therefore,

surface area = 2(lw + wh + lh)

surface area = 2(7.5×5 + 5×8 + 7.5×8)

surface area = 2(37.5 + 40 + 60)

surface area = 2(137.5 )

surface area = 275 ft²

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