11.09.2021

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY MIND A cup has the shape of a right circular cone. The height of the cup is 16 cm, and the radius of the
cm opening is 4 cm. Water is being poured into the cup at a constant rate of 3 cm. At what rate, in
cm per second, is the water level rising when the depth of the water in the cup is 6 cm? (The volume of a cone of height h and radius r is given by V=1/3pir^2h.

1. 1/64pi
2. 3/pi
3. 4/3pi
4. 9/4pi

. 0

Step-by-step answer

09.07.2023, solved by verified expert
Unlock the full answer

3.  PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

Step-by-step explanation:

Volume of a cone:

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

(where r is the radius and h is the height)

Given:

h = 16 cmr = 4 cm

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

Therefore, substitute PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42 into the volume formula to find the volume of the cone in terms of h:

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

Differentiate with respect to h:

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

Volume is increasing at a constant rate of 3cm/s:

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

Use the chain rule to find PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

When h = 6:

PLEASE HELP THIS IS AP CALCULUS IM LOSING MY, №18011166, 11.09.2021 13:42

It is was helpful?

Faq

Mathematics
Step-by-step answer
P Answered by Specialist

3.  \dfrac{4}{3 \pi}

Step-by-step explanation:

Volume of a cone:

V=\dfrac13\pi r^2h

(where r is the radius and h is the height)

Given:

h = 16 cmr = 4 cm

\implies r=\dfrac14h

Therefore, substitute r=\frac14h into the volume formula to find the volume of the cone in terms of h:

\implies V=\dfrac13\pi \left(\dfrac14h\right)^2h

\implies V=\dfrac{1}{48}\pi h^3

Differentiate with respect to h:

\implies \dfrac{dV}{dh}=3 \cdot \dfrac{1}{48} \pi h^2=\dfrac{\pi h^2}{16}

Volume is increasing at a constant rate of 3cm/s:

\implies \dfrac{dV}{dt}=3

Use the chain rule to find \dfrac{dh}{dt}

\implies \dfrac{dh}{dt}=\dfrac{dV}{dt}\times\dfrac{dh}{dV}

\implies \dfrac{dh}{dt}=3\times\dfrac{16}{\pi h^2}

\implies \dfrac{dh}{dt}=\dfrac{48}{\pi h^2}

When h = 6:

\implies \dfrac{dh}{dt}=\dfrac{48}{\pi \cdot 6^2}=\dfrac{4}{3 \pi}

Mathematics
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 
Mathematics
Step-by-step answer
P Answered by PhD

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

Mathematics
Step-by-step answer
P Answered by PhD
The answer is in the image 

The answer is in the image 

Mathematics
Step-by-step answer
P Answered by PhD

The solution is given in the image below

The solution is given in the image below
Mathematics
Step-by-step answer
P Answered by PhD

Speed=Distance/time

Here,

distance=15m

time=1sec

speed=15/1=15m/sec

Distance=Speed*time

time=15min=15*60sec=900sec

Distance travelled in 15 min=15*900=13,500m

=13500/1000 km=13.5Km

Mathematics
Step-by-step answer
P Answered by PhD

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.

Mathematics
Step-by-step answer
P Answered by PhD

tip=18% of 75.45

     =18/100 * 75.45 = $13.581

Tip = $13.581

Mathematics
Step-by-step answer
P Answered by PhD

Volume of rectangular prism=length * width * height

Given,

length=3/8cm

breadth=5/8cm

height=7/8cm

therefore volume=(3/8)*(5/8)*(7/8)

                           =105/512 cm3

Try asking the Studen AI a question.

It will provide an instant answer!

FREE