Sure, let's solve the problem step-by-step to find the volume of Tommy's first soup can, which has a radius of 2 inches and a height of 6 inches.
1. Write the formula for the area of a circle to find the base area [tex]\( B \)[/tex]:
The area of a circle is given by the formula:
[tex]\[
B = \pi r^2
\][/tex]
2. Substitute the actual measures for the radius [tex]\( r \)[/tex]:
Given the radius [tex]\( r = 2 \)[/tex] inches, we have:
[tex]\[
B = \pi (2^2)
\][/tex]
3. Evaluate the power:
[tex]\[
B = \pi (4)
\][/tex]
So, the base area [tex]\( B \)[/tex] of the cylinder is:
[tex]\[
B = 4\pi \quad \text{square inches}
\][/tex]
Numerically, substituting the value of [tex]\( \pi \approx 3.14159 \)[/tex], we get:
[tex]\[
B \approx 4 \times 3.14159 = 12.566370614359172 \quad \text{square inches}
\][/tex]
4. Write the formula for the volume of a cylinder [tex]\( V \)[/tex] using the base area [tex]\( B \)[/tex] and height [tex]\( h \)[/tex]:
The volume of a cylinder is given by:
[tex]\[
V = B \times h
\][/tex]
5. Substitute the base area [tex]\( B \)[/tex] and the given height [tex]\( h \)[/tex]:
Given the height [tex]\( h = 6 \)[/tex] inches, we have:
[tex]\[
V = 12.566370614359172 \times 6
\][/tex]
6. Simplify the expression:
[tex]\[
V = 75.39822368615503 \quad \text{cubic inches}
\][/tex]
So, the volume of Tommy's first soup can is:
The base area [tex]\( B \)[/tex] is approximately [tex]\( 12.57 \)[/tex] square inches.
The volume [tex]\( V \)[/tex] of the cylinder is approximately [tex]\( 75.40 \)[/tex] cubic inches.
To summarize:
- Base Area [tex]\( B \approx 12.57 \)[/tex] square inches
- Volume [tex]\( V \approx 75.40 \)[/tex] cubic inches
