Help with this!!

Question

The volume V of a rectangular prism of a particular height varies jointly as the length x and the width w, and V = 224 ft3 when x = 8 ft and w = 4 ft. Write the variation function, and then find x when V = 210 ft3 and w = 5 ft.

Answer 1

Aracely,

Joint variation means that V = kxw for some value of k.

Plug in the given values to find k. Then use this value of k to answer the question.

Answer 2

The volume of a rectangular prism is the product of the length, the width and the height of the prism. The formula looks like this: V = l x w x h. This is the variation function.

To find the length of the prism in your problem, plug in the values for height, width, and volume.

224 = 8 x 4 x h

h x 8 x 4 = 224

h = 224/(8 x 4) = 7

Therefore, the height of the rectangular prism with a volume of 224ft², width of 4ft, and length of 8ft is 7 ft.

If we have a rectangular prism with the same height but with a volume of 210ft³ and a width of 5ft, we can find the length (x) by plugging the other values into the formula (V = l x w x h).

210 = l x 5 x 7

l x 5 x 7 = 210

l = 210/(5 x 7) = 6

The length of the second rectangular prism is 6ft.