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.
V= areabase*height= length*width*height
To find the length (l) when V = 210 ft and w = 5 ft, we can use the formula for joint variation.
In joint variation, the volume (V) is directly proportional to the length (l) and the width (w). This can be written as:
V = k * l * w
where k is a constant.
We are given that V = 224 ft when l = 8 ft and w = 4 ft. Let's use this information to find the value of k:
224 = k * 8 * 4
224 = k * 32
k = 224 / 32
k = 7
Now that we have the value of k, we can use it to find l when V = 210 ft and w = 5 ft:
210 = 7 * l * 5
210 = 35l
l = 210 / 35
l = 6
Therefore, when V = 210 ft and w = 5 ft, the length (l) of the rectangular prism is 6 ft.
To find the value of l when V = 210 ft and w = 5 ft, we can use the concept of joint variation.
In this problem, we are given that the volume V of a rectangular prism varies jointly as the length l and the width w. Mathematically, this can be represented as:
V = k * l * w
Where k is the constant of variation.
To find the value of k, we can use the given information that V = 224 ft when l = 8 ft and w = 4 ft. Plugging these values into the equation, we get:
224 = k * 8 * 4
Dividing both sides of the equation by 32, we find that k = 7.
So, the equation representing the joint variation is:
V = 7lw
Now, we can use this equation to find the value of l when V = 210 ft and w = 5 ft. Plugging these values into the equation, we get:
210 = 7l * 5
Dividing both sides of the equation by 35, we find:
l = 6
Therefore, when V = 210 ft and w = 5 ft, the value of l is 6 ft.