The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.6 in/s. At what rate is the volume of the cone changing when the radius is 107 in. and the height is 151 in.

The volume of the cone is increasing at a rate of 1926 cubic inches per second.

Step-by-step explanation:

Volume of a right circular cone:

The volume of a right circular cone, with radius r and height h, is given by the following formula:

Implicit derivation:

To solve this question, we have to apply implicit derivation, derivating the variables V, r and h with regard to t. So

Radius is 107 in. and the height is 151 in.

This means that

The radius of a right circular cone is increasing at a rate of 1.1 in/s while its height is decreasing at a rate of 2.6 in/s.

This means that

At what rate is the volume of the cone changing when the radius is 107 in. and the height is 151 in.

This is . So

Positive, so increasing.

The volume of the cone is increasing at a rate of 1926 cubic inches per second.

2 over 5

step-by-step explanation:

the 2: 3 ratio is the length of the ac segment to the cb segment total length. this implies that the ratio between segment ac length and segment ab length is 2: 5. point c is 2/5 from a to b, so the required fraction is 2/5.

15 units use socratic

step-by-step explanation: 15 units