Question

Ryan made two similar glass display boxes shaped like triangular prisms. The length of the sides of the base of the first display box is 2 feet, and the length of the sides of the base of the second display box is 6 feet. If the volume of the first display box is 24 ft3, what is the volume of the second display box?
Answer

288 ft3

648 ft3

724 ft3

864 ft3

Answer 1

648 ft3

Answer 2

how did you get that? like how did you work it out?

Answer 3

and thank-you

Answer 4

The scale factor of the two similar boxes is 2/6 or 1/3.

If two solids are similar, the cube of the scale factor = the ratio of the volumes.

(1/3)^3 = 24/V where V is the volume of the larger solid.

1/27 = 24/v

V = 27*24 = 648

Answer 5

oh ok thank-you so much!