Mathematics, 18.06.2021 04:40 johnsonkia873

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.

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Answer from: samantha9430

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:

$V = \frac{1}{3} \pi r^2h$

Implicit derivation:

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

$\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)$

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

This means that r = 107, h = 151

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 $\frac{dr}{dt} = 1.1, \frac{dh}{dt} = -2.6$

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

This is $\frac{dV}{dt}$ . So

$\frac{dV}{dt} = \frac{1}{3}\left(2rh\frac{dr}{dt} + r^2\frac{dh}{dt}\right)$

$\frac{dV}{dt} = \frac{1}{3}(2(107)(151)(1.1) + (107)^2(-2.6))$

$\frac{dV}{dt} = \frac{2(107)(151)(1.1) - (107)^2(2.6)}{3}$

$\frac{dV}{dt} = 1926$

Positive, so increasing.

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

Answer from: Quest

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200. after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes 1800 - 6400 which gets you 11,600.

Answer from: Quest

Gggģcawrygr3ezt9d hu and the other countries have been working to make it easier to box up their homes in an area where the government has not yet decided which countries will have the option of the government

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