Question

the volume (v) of a cone varies jointly as the height (h) of the cone and the area of the base (b). a cone has a volume of 140 with height 15 and base 28. find the volume of a cone with height 7 and base 12.

Answer 1

Using the formula for joint variation, the constant of proportionality (k) is determined from the given cone's dimensions. Applying k to the dimensions of the new cone, the volume is found to be 28 cubic units.

Step-by-step explanation:

The volume (V) of a cone is said to vary jointly as the height (h) of the cone and the area of the base (b). This means that we can express the relationship as V = k * b * h, where k is the constant of proportionality. Given that a cone has a volume of 140 with height 15 and base 28, we first need to find the value of k using the formula V = k * b * h.

We first calculate k as follows:

140 = k * 28 * 15

k = 140 / (28 * 15)

k = 0.333... (repeating)

Now, we can find the volume of a new cone with height 7 and base 12:

V = k * b * h

V = 0.333... * 12 * 7

V = 28 (cubic units)

Therefore, the volume of the cone with height 7 and base 12 is 28 cubic units.