Question

After all of this gardening work, Geoffrey decides he needs a new shed to replace the old one. His current shed is a rectangular prism that measures 6 feet long by 5 feet wide by 8 feet high. He realizes he needs a shed with 480 cubic feet of storage.

a. Will he achieve his goal if he doubles each dimension? Why or why not?
b. If he wants to keep the height the same, what could the other dimensions be for him to get the volume he wants?
c. If he uses the dimensions in part (b), what could be the area of the new shed’s floor?

Answer 1

A. No.

B. 15 ft x 12 ft

C. 180 Square ft

Explanation:

A. Doubling each dimension, the new measurements would be 10 ft

12 ft and

16 ft.

The volume of the new shed would be

V = 1/3 Bh

B = base of the floor

h = height

Base of the floor is 10 feet time 12 feet equals 120 square feet.

V= 1/3 (120)(16)

V= 640 cubic feet. Which is greater than 480 cubic feet.

B. If he keeps the height of the shed the same (8 feet) he would have to increase the area of the floor by 6.

A way of doing that is multiplying 5 by 3 and 6 by 2. Then the new floor is 15 ft by 12 feet.

V= 1/3 Bh

B=15X12=180 Square feet.

V= 1/3 (180)(8)

V= 480 cubic feet.

C. 15 x 12 =180 Square feet.