Direct and Joint Variation
2. The volume V of a rectangular prism of a particular height varies jointly as the length l and the width w, and V = 224 ft when l = 8 ft and w = 4 ft.
Find l when V = 210 ft and w = 5 ft.
see below.
To find the value of l when V = 210 ft and w = 5 ft, we need to use the formula for direct and joint variation.
In this case, we are given that the volume V of the rectangular prism varies jointly as the length l and the width w. This can be represented by the equation:
V = k * l * w
Where k is the constant of variation.
We are given one set of values: V = 224 ft, l = 8 ft, and w = 4 ft. Plugging these values into the equation, we can solve for k:
224 = k * 8 * 4
224 = 32k
To solve for k, we divide both sides of the equation by 32:
k = 224 / 32
k = 7
Now that we have the value of k, we can use it to find the value of l when V = 210 ft and w = 5 ft. Plugging these values into the equation, we have:
210 = 7 * l * 5
To solve for l, we divide both sides of the equation by 7 * 5:
210 / (7 * 5) = l
6 = l
Therefore, the value of l when V = 210 ft and w = 5 ft is 6 ft.