A washing machine is being redesigned to handle a greater volume of water. One part is a pipe with a radius of 3 centimeters (cm) and a length of 11cm. It gets replaced with a pipe of radius 4cm, and the same length. The new pipe can hold w pi more cubic centimeters (cm^(3)) of water than the old pipe, where w is a constant. What is the value of w ?

Calculate volume of old pipe: Calculate the volume of the old pipe. The volume of a cylinder (pipe) is given by the formula V = πr^2h, where r is the radius and h is the height (or length) of the cylinder. For the old pipe, r = 3 cm and h = 11 cm. V_old = π * (3 cm)^2 * 11 cm = π * 9 cm^2 * 11 cm = 99π cm^3.Calculate volume of new pipe: Calculate the volume of the new pipe. For the new pipe, r = 4 cm and h = 11 cm (same as the old pipe). V_new = π * (4 cm)^2 * 11 cm = π * 16 cm^2 * 11 cm = 176π cm^3.Calculate difference in volume: Calculate the difference in volume between the new pipe and the old pipe. The difference in volume will be the volume of the new pipe minus the volume of the old pipe. Difference = V_new - V_old = 176π cm^3 - 99π cm^3 = (176 - 99)π cm^3 = 77π cm^3.Identify value of w: Identify the value of w from the difference in volume. The problem states that the new pipe can hold wπ more cubic centimeters of water than the old pipe. Therefore, wπ = 77π cm^3. To find w, we divide both sides of the equation by π. w = 77π cm^3 / π = 77.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A washing machine is being redesigned to handle a greater volume of water. One part is a pipe with a radius of 3 centimeters
(cm) and a length of
11cm. It gets replaced with a pipe of radius
4cm, and the same length. The new pipe can hold
w pi more cubic centimeters
(cm^(3)) of water than the old pipe, where
w is a constant. What is the value of
w ?

A washing machine is being redesigned to handle a greater volume of water. One part is a pipe with a radius of $3$ centimeters $(\mathrm{cm})$ and a length of $11 \mathrm{~cm}$ . It gets replaced with a pipe of radius $4 \mathrm{~cm}$ , and the same length. The new pipe can hold $w \pi$ more cubic centimeters $\left(\mathrm{cm}^{3}\right)$ of water than the old pipe, where $w$ is a constant. What is the value of $w$ ?

View step-by-step help

Home

Math Problems

Algebra 1

Solve a system of equations using substitution: word problems

Full solution

Q. A washing machine is being redesigned to handle a greater volume of water. One part is a pipe with a radius of

3

centimeters

(\mathrm{cm})

and a length of

11 \mathrm{~cm}

. It gets replaced with a pipe of radius

4 \mathrm{~cm}

, and the same length. The new pipe can hold

w \pi

more cubic centimeters

\left(\mathrm{cm}^{3}\right)

of water than the old pipe, where

w

is a constant. What is the value of

w

Calculate volume of old pipe: Calculate the volume of the old pipe. $\newline$ The volume of a cylinder (pipe) is given by the formula $V = \pi r^2 h$ , where $r$ is the radius and $h$ is the height (or length) of the cylinder. $\newline$ For the old pipe, $r = 3$ cm and $h = 11$ cm. $\newline$ $V_{\text{old}} = \pi \times (3\,\text{cm})^2 \times 11\,\text{cm} = \pi \times 9\,\text{cm}^2 \times 11\,\text{cm} = 99\pi\,\text{cm}^3$ .
Calculate volume of new pipe: Calculate the volume of the new pipe. $\newline$ For the new pipe, $r = 4\,\text{cm}$ and $h = 11\,\text{cm}$ (same as the old pipe). $\newline$ $V_{\text{new}} = \pi \times (4\,\text{cm})^2 \times 11\,\text{cm} = \pi \times 16\,\text{cm}^2 \times 11\,\text{cm} = 176\pi\,\text{cm}^3$ .
Calculate difference in volume: Calculate the difference in volume between the new pipe and the old pipe. $\newline$ The difference in volume will be the volume of the new pipe minus the volume of the old pipe. $\newline$ Difference = $V_{\text{new}} - V_{\text{old}} = 176\pi \text{ cm}^3 - 99\pi \text{ cm}^3 = (176 - 99)\pi \text{ cm}^3 = 77\pi \text{ cm}^3$ .
Identify value of $w$ : Identify the value of $w$ from the difference in volume. $\newline$ The problem states that the new pipe can hold $w\pi$ more cubic centimeters of water than the old pipe. $\newline$ Therefore, $w\pi = 77\pi$ cm $^3$ . $\newline$ To find $w$ , we divide both sides of the equation by $\pi$ . $\newline$ $w = \frac{77\pi \text{ cm}^3}{\pi} = 77$ .