Find the surface area of the cylinder to the nearest whole number. The figure is not drawn to scale.
13 in on top, 14 in around/
The answer is 2,205 inches squared
To find the surface area of the cylinder, we need to add the areas of the two bases and the lateral surface area.
1. The area of each base of the cylinder is given by the formula for the area of a circle: A = πr^2, where r is the radius of the base.
Given that the diameter of the base is 13 inches, we can find the radius by dividing the diameter by 2:
r = 13/2 = 6.5 inches
The area of each base is:
A_base = π(6.5)^2
2. The lateral surface area of the cylinder is given by the formula: A_lateral = 2πrh, where r is the radius of the base and h is the height of the cylinder.
The circumference of the base is 14 inches, which means the lateral height is also 14 inches.
The lateral surface area is:
A_lateral = 2π(6.5)(14)
3. Now we can calculate the total surface area by adding the areas of the two bases and the lateral surface area:
A_total = 2(A_base) + A_lateral
Substituting the values:
A_total = 2[π(6.5)^2] + 2π(6.5)(14)
Calculating the surface area using a calculator:
A_total ≈ 846 square inches (rounded to the nearest whole number)
Therefore, the surface area of the cylinder to the nearest whole number is 846 square inches.
To find the surface area of a cylinder, you need to sum the areas of the two circular bases and the lateral surface area. Let's break it down step by step:
1. Calculate the area of the circular bases:
- The formula for the area of a circle is A = π * r², where A is the area and r is the radius.
- Given the figure is not drawn to scale, we assume that the radius of the circular bases is half the diameter.
- The top base has a diameter of 13 inches, so the radius is 13 / 2 = 6.5 inches.
- Area of the top base = π * (6.5)².
- The circumference of the cylinder is 14 inches, which means the base's circumference is 14 inches.
- The radius can be found by dividing the circumference by 2π: r = 14 / (2π) ≈ 14 / 6.28 ≈ 2.23 inches.
- Area of the bottom base = π * (2.23)².
2. Calculate the lateral surface area:
- The lateral surface area of a cylinder is given by the formula A = 2πrh, where A is the area, r is the radius, and h is the height.
- Since the height is not provided in the question, we can't calculate the exact surface area. However, we can find an approximate answer.
3. Approximating the surface area:
- Since the figure is not drawn to scale, we'll have to estimate the height of the cylinder based on the given measurements.
- Let's assume the height is 12 inches.
- Lateral surface area = 2π * 6.5 * 12.
4. Sum the areas:
- Surface area = area of top base + area of bottom base + lateral surface area.
Now, you can substitute the values into the formulas and calculate the approximate surface area of the cylinder.
is that 13 in high?
Presumably the circular top has the same circumference as the cylinder.