Question
The canister has a height of 7 inches and a radius of 4 inches. How much material was used to make the canister? (Use 3.14 for .)
Answers
GPT-4o mini
To find the amount of material used to make the canister, we first need to calculate its surface area. A canister is typically in the shape of a cylinder, so we will use the formula for the surface area of a cylinder, which includes the lateral surface area and the area of the two circular bases.
The formula for the surface area \( A \) of a cylinder is given by:
\[
A = 2\pi rh + 2\pi r^2
\]
where:
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is a constant (approximately 3.14).
Given:
- Radius \( r = 4 \) inches,
- Height \( h = 7 \) inches.
Now we can plug in the values into the formula.
1. **Calculate the lateral surface area**:
\[
2\pi rh = 2 \times 3.14 \times 4 \times 7
\]
Calculating that step-by-step:
\[
2 \times 3.14 = 6.28
\]
\[
6.28 \times 4 = 25.12
\]
\[
25.12 \times 7 = 175.84
\]
So, the lateral surface area is:
\[
175.84 \text{ square inches}
\]
2. **Calculate the area of the bases**:
\[
2\pi r^2 = 2 \times 3.14 \times 4^2
\]
Calculating that step-by-step:
\[
4^2 = 16
\]
\[
2 \times 3.14 = 6.28
\]
\[
6.28 \times 16 = 100.48
\]
So, the area of the two bases is:
\[
100.48 \text{ square inches}
\]
3. **Total surface area**:
Now, we add the lateral surface area and the area of the two bases together:
\[
A = 175.84 + 100.48 = 276.32
\]
Therefore, the total amount of material used to make the canister is:
\[
\boxed{276.32} \text{ square inches}
\]
The formula for the surface area \( A \) of a cylinder is given by:
\[
A = 2\pi rh + 2\pi r^2
\]
where:
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is a constant (approximately 3.14).
Given:
- Radius \( r = 4 \) inches,
- Height \( h = 7 \) inches.
Now we can plug in the values into the formula.
1. **Calculate the lateral surface area**:
\[
2\pi rh = 2 \times 3.14 \times 4 \times 7
\]
Calculating that step-by-step:
\[
2 \times 3.14 = 6.28
\]
\[
6.28 \times 4 = 25.12
\]
\[
25.12 \times 7 = 175.84
\]
So, the lateral surface area is:
\[
175.84 \text{ square inches}
\]
2. **Calculate the area of the bases**:
\[
2\pi r^2 = 2 \times 3.14 \times 4^2
\]
Calculating that step-by-step:
\[
4^2 = 16
\]
\[
2 \times 3.14 = 6.28
\]
\[
6.28 \times 16 = 100.48
\]
So, the area of the two bases is:
\[
100.48 \text{ square inches}
\]
3. **Total surface area**:
Now, we add the lateral surface area and the area of the two bases together:
\[
A = 175.84 + 100.48 = 276.32
\]
Therefore, the total amount of material used to make the canister is:
\[
\boxed{276.32} \text{ square inches}
\]