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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