Question

The Gardening Club is looking to build a new greenhouse at their school with the dimensions shown below.

Volume and circles !

Answer 1

a) 2,400 ft^3

b) 1,413 ft^3

c) 3,813 ft^3

Explanation:

First, two general equations:

For a rectangular prism of length L, width W and height H, the volume is:

V = L*W*H

And for a cylinder of radius R and height H, the volume is:

V = pi*(R^2)*H

where pi = 3.14

a) First we want to find the area of the rectangular part.

We can see that the measures are:

H = 8ft

W = 12ft

L = 25ft

Then the volume of this part is:

V = (8ft)*(12ft)*(25ft) = 2,400 ft^3

b) For the half-cylinder, we can see that we have a diameter of 12ft (then has a radius of 12ft/2 = 6ft) and a height of 25ft

R = 6ft

H = 25ft

Then the volume of this part will be half of the volume of a cylinder with these dimensions, so here we have:

V' = (3.14*(6ft)^2*25ft)/2 = 1,413 ft^3

c) The total volume is just the sum of the two volumes we found above, this is:

Volume = V + V' = 2,400 ft^3 + 1,413 ft^3 = 3,813 ft^3