Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The conical tank shown here is filled with olive oil weighing
41lb//ft^(3). How much work does it take to pump all of the oil to the rim of the tank?

W=
◻
ft-lb (Round to the nearest whole number as needed.)

The conical tank shown here is filled with olive oil weighing $41 \mathrm{lb} / \mathrm{ft}^{3}$ . How much work does it take to pump all of the oil to the rim of the tank? $\newline$ $W=$ $\square$ $\mathrm{ft}-\mathrm{lb}$ (Round to the nearest whole number as needed.)

View step-by-step help

View step-by-step help

Circles: word problems

Full solution

Q. The conical tank shown here is filled with olive oil weighing

41 \mathrm{lb} / \mathrm{ft}^{3}

. How much work does it take to pump all of the oil to the rim of the tank?

\newline

W=

\square

\mathrm{ft}-\mathrm{lb}

(Round to the nearest whole number as needed.)

Find Volume of Tank: First, we need to find the volume of the conical tank to determine how much oil it holds. Assume the tank has a height $h$ and a radius $r$ at the top. The formula for the volume of a cone is $V = \frac{1}{3}\pi r^2 h$ .
Calculate Weight of Oil: Next, calculate the weight of the olive oil in the tank. Given the density of olive oil is $41 \, \text{lb/ft}^3$ , multiply this by the volume of the tank to find the total weight. Weight = Density $\times$ Volume = $41 \, \text{lb/ft}^3 \times V$ .
Calculate Work Done: To find the work done to pump the oil to the rim, use the work formula $W = \text{Weight} \times \text{Distance}$ . Here, the distance is the height of the tank, $h$ , since we're pumping to the rim. $W = 41V \times h$ .

More problems from Circles: word problems

Question

Skyler climbs a watchtower to guard against forest fires.

\newline

R(h)=\sqrt{13h}

gives the distance, in kilometers, that Skyler can see when their eyes are

h

meters above the ground.

\newline

A(d)=\pi d^{2}

gives the area, in square kilometers, that Skyler can guard when they can see a distance of

d

\newline

Which expression models the area Skyler can guard when their eyes are

h

meters above the ground?

\newline

1

\newline

13\pi h

\newline

13\pi h^{2}

\newline

\sqrt{13\pi h^{2}}

\newline

169\pi h^{2}

Posted 2 months ago

Question

After the outbreak of a mysterious disease, the average wait time at a hospital increased by

70\%

. Before the outbreak, the average wait time at the hospital was

m

\newline

Which of the following expressions could represent the average wait time at the hospital after the outbreak?

\newline

2

\newline

0.7m

\newline

\frac{170}{100}m

\newline

m+70

\newline

m+0.7

\newline

1.7m

Posted 1 month ago

Question

The radius of a semicircle is

3

yards. What is the semicircle's area?

\newline

\pi \approx 3.14

and round your answer to the nearest hundredth.

\newline

Posted 2 months ago

Question

\newline

A man has bent a circular wire of radius

49\text{cm}

to form a square. Find the sides of a square.

\newline

A)100\text{cm}

\newline

B)50\text{cm}

\newline

C)98\text{cm}

Posted 2 months ago

Question

A quarter is worth

\$0.25

and a half dollar is worth

\$0.50

\newline

a. A quarter has a diameter of

\frac{15}{16}

inch and a height of

\frac{1}{16}

inch. Find the surface area of a quarter. Round your answer to the nearest hundredth.

\newline

b. A half dollar has a diameter of

\frac{9}{8}

inches and a height of

\frac{3}{32}

inch. Find the surface area of a half dollar. Round your answer to the nearest hundredth.

Posted 2 months ago

Question

The hypotenuse of a right triangle measures

17 \mathrm{~cm}

and one of its legs measures

8 \mathrm{~cm}

. Find the measure of the other leg. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 3 months ago

Question

One of the legs of a right triangle measures

15 \mathrm{~cm}

and its hypotenuse measures

17 \mathrm{~cm}

. Find the measure of the other leg. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 3 months ago

Question

One of the legs of a right triangle measures

8 \mathrm{~cm}

and the other leg measures

15 \mathrm{~cm}

. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

\newline

\square

\mathrm{cm}

Posted 3 months ago

Question

Find the volume of a right circular cone that has a height of

7.4 \mathrm{~cm}

and a base with a radius of

8.1 \mathrm{~cm}

. Round your answer to the nearest tenth of a cubic centimeter.

\newline

\mathrm{cm}^{3}

Posted 3 months ago

Question

Find the volume of a right circular cone that has a height of

13.3 \mathrm{ft}

and a base with a diameter of

9.4 \mathrm{ft}

. Round your answer to the nearest tenth of a cubic foot.

\newline

\mathrm{ft}^{3}

Posted 3 months ago