Question
Mary baked a cake in the shape of a cylinder with a diameter of 8 inches and a height of 10 inches. She wants to cover the entire cake (including the bottom so it will stick to the plate) with icing.
Complete these steps to determine the surface area of Mary's cake.
(1 point)
radius =
inches
Question 2
The area of a circle is πr2
. Use 3.14 for π
. Do not round.(1 point)
area of the top circular base=
square inches
Question 3
(1 point)
area of the bottom circular base =
square inches
Question 4
(1 point)
total area of circular bases (add the areas) =
square inches
Question 5
Remember that the area of the lateral rectangular face is the circumference of the circle (2π
r) multiplied by the height of the cylinder.
Use 3.14 for π
. Do not round.
(1 point)
circumference of the circular base =
square inches
Question 6
(1 point)
height of the cylinder =
inches
Question 7
(1 point)
area of the lateral face (circumference x height) =
square inches
Question 8
Find the Surface Area of the cylinder. Do not round.
Surface area = total area of circular bases + area of lateral rectangular face.
(3 points)
Surface Area =
(total area of circular bases) +
(area of lateral rectangular face) =
square inches
Answers
GPT-4o mini
To solve for the surface area of Mary's cake (which is in the shape of a cylinder), we can follow the steps as outlined.
### Question 1
**radius =**
- The diameter of the cake is 8 inches, so the radius is half of that.
- radius = 8 inches / 2 = **4 inches**
### Question 2
**area of the top circular base =**
- The area of a circle is given by the formula \( A = \pi r^2 \).
- Using \( \pi = 3.14 \):
\[
\text{area of the top circular base} = 3.14 \times (4)^2 = 3.14 \times 16 = 50.24 \text{ square inches}
\]
### Question 3
**area of the bottom circular base =**
- Because the bottom base is the same size as the top base, its area will also be:
\[
\text{area of the bottom circular base} = 50.24 \text{ square inches}
\]
### Question 4
**total area of circular bases (add the areas) =**
- Total area of circular bases = area of top + area of bottom:
\[
\text{total area of circular bases} = 50.24 + 50.24 = 100.48 \text{ square inches}
\]
### Question 5
**circumference of the circular base =**
- The circumference is given by the formula \( C = 2\pi r \).
\[
\text{circumference} = 2 \times 3.14 \times 4 = 25.12 \text{ inches}
\]
### Question 6
**height of the cylinder =**
- The height was given in the problem statement as **10 inches**.
### Question 7
**area of the lateral face (circumference x height) =**
- The area of the lateral face is the circumference times the height:
\[
\text{area of the lateral face} = 25.12 \times 10 = 251.2 \text{ square inches}
\]
### Question 8
**Find the Surface Area of the cylinder.**
- Surface Area = total area of circular bases + area of lateral rectangular face:
\[
\text{Surface Area} = 100.48 + 251.2 = 351.68 \text{ square inches}
\]
### Summary of Answers:
1. radius = **4 inches**
2. area of the top circular base = **50.24 square inches**
3. area of the bottom circular base = **50.24 square inches**
4. total area of circular bases = **100.48 square inches**
5. circumference of the circular base = **25.12 square inches**
6. height of the cylinder = **10 inches**
7. area of the lateral face = **251.2 square inches**
8. Surface Area = **351.68 square inches**
### Question 1
**radius =**
- The diameter of the cake is 8 inches, so the radius is half of that.
- radius = 8 inches / 2 = **4 inches**
### Question 2
**area of the top circular base =**
- The area of a circle is given by the formula \( A = \pi r^2 \).
- Using \( \pi = 3.14 \):
\[
\text{area of the top circular base} = 3.14 \times (4)^2 = 3.14 \times 16 = 50.24 \text{ square inches}
\]
### Question 3
**area of the bottom circular base =**
- Because the bottom base is the same size as the top base, its area will also be:
\[
\text{area of the bottom circular base} = 50.24 \text{ square inches}
\]
### Question 4
**total area of circular bases (add the areas) =**
- Total area of circular bases = area of top + area of bottom:
\[
\text{total area of circular bases} = 50.24 + 50.24 = 100.48 \text{ square inches}
\]
### Question 5
**circumference of the circular base =**
- The circumference is given by the formula \( C = 2\pi r \).
\[
\text{circumference} = 2 \times 3.14 \times 4 = 25.12 \text{ inches}
\]
### Question 6
**height of the cylinder =**
- The height was given in the problem statement as **10 inches**.
### Question 7
**area of the lateral face (circumference x height) =**
- The area of the lateral face is the circumference times the height:
\[
\text{area of the lateral face} = 25.12 \times 10 = 251.2 \text{ square inches}
\]
### Question 8
**Find the Surface Area of the cylinder.**
- Surface Area = total area of circular bases + area of lateral rectangular face:
\[
\text{Surface Area} = 100.48 + 251.2 = 351.68 \text{ square inches}
\]
### Summary of Answers:
1. radius = **4 inches**
2. area of the top circular base = **50.24 square inches**
3. area of the bottom circular base = **50.24 square inches**
4. total area of circular bases = **100.48 square inches**
5. circumference of the circular base = **25.12 square inches**
6. height of the cylinder = **10 inches**
7. area of the lateral face = **251.2 square inches**
8. Surface Area = **351.68 square inches**