Question - Calculating the Circumference of a Cylinder's Base
Solution:
The volume \( V \) of a cylinder is given by \( V = \pi r^2 h \) where \( r \) is the radius and \( h \) is the height.
Given:
\( V = 12,936 \text{ cm}^3 \)
\( h = 21 \text{ cm} \)
\( \pi \approx \frac{22}{7} \)
To find the circumference \( C \), we need to find the radius \( r \) first.
From the volume formula:
\( 12,936 = \frac{22}{7} \times r^2 \times 21 \)
Solving for \( r^2 \):
\( r^2 = \frac{12,936 \times 7}{22 \times 21} \)
\( r^2 = \frac{12,936}{66} \)
\( r^2 = 196 \)
\( r = \sqrt{196} \)
\( r = 14 \text{ cm} \)
Now we calculate the circumference \( C \) using the radius \( r \):
\( C = 2 \pi r \)
\( C = 2 \times \frac{22}{7} \times 14 \)
\( C = 88 \text{ cm} \)
Therefore, the circumference of the base of the cylinder is \( 88 \text{ cm} \).
Tutor Solution:
First, we isolate \( r^2 \) by dividing both sides by \( \left(\frac{22}{7}\right) \) and by 21:
\[ r^2 = \frac{12,936}{\left(\frac{22}{7}\right) \times 21} \]To perform the division, you multiply by the reciprocal of the fraction:
\[ r^2 = \frac{12,936}{22} \times \frac{7}{21} \]This simplifies to:
\[ r^2 = 588 \times \frac{1}{3} \]So then, we have:
\[ r^2 = 196 \]Now take the square root of both sides to find \( r \):
\[ r = \sqrt{196} \] \[ r = 14 \text{ cm} \]The circumference of the base, \( C \), is given by the formula:
\[ C = 2\pi r \]Using the given value of \( \pi \) and the radius we just calculated:
\[ C = 2 \times \left(\frac{22}{7}\right) \times 14 \]Which simplifies to:
\[ C = 2 \times 22 \times 2 \] \[ C = 88 \text{ cm} \]Therefore, the circumference of the base of the cylinder is 88 cm.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com