Question

The volume V of a rectangular prism of a particular height varies jointly as the length L and the width W, and V=224ft³ when L=8ft and w=4ft. Find L when V=210ft³ and w=5ft

Answer 1

To find the length L when the volume V equals 210 ft³ and the width W is 5 ft, we first find the proportionality constant k from the given values, and then solve for L with the new volume and width.

Step-by-step explanation:

The volume V of a rectangular prism is directly proportional to its length L and width W. Given that V = 224 ft³ when L = 8 ft and W = 4 ft, we can find the constant of proportionality, k, using the formula V = k × L × W. Calculating k we get:

k = V / (L × W) = 224 / (8 × 4) = 7.

Now, when V = 210 ft³ and W = 5 ft, we can find the new length L using the original proportionality constant:

210 = 7 × L × 5L = 210 / (7 × 5)L = 6 ft

Therefore, the length L when the volume is 210 ft³ and width is 5 ft is 6 ft.