Question

What is the total surface area of the pencil sharpener? Your answer should have two decimal places.
6 cm
5.77 cm
15 cm
6.5 cm

Answer 1

Wrong

Answer 2

The total surface area of the pencil sharpener can be calculated by first finding the surface area of each part and then adding them together.

The formula for the surface area of a cylinder is 2πr(r+h), where r is the radius and h is the height.

Given that the radius (r) of the pencil sharpener is 6 cm and the height (h) is 5.77 cm, we can calculate the surface area of the cylinder:

Surface Area = 2π(6)(6+5.77)
Surface Area = 2π(6)(11.77)
Surface Area ≈ 442.73 cm²

Now, we need to add the surface area of the circular base of the cylinder. The formula for the surface area of a circle is πr².

Surface Area of the circular base = π(6)²
Surface Area of the circular base ≈ 113.10 cm²

Adding both values give us the total surface area:

Total Surface Area ≈ 442.73 cm² + 113.10 cm²
Total Surface Area ≈ 555.83 cm²

Therefore, the total surface area of the pencil sharpener is approximately 555.83 cm².

Answer 3

Apologies for the mistake. Let's recalculate the total surface area of the pencil sharpener.

The pencil sharpener consists of the curved surface area of the cylinder and the two circular bases.

Given:
Radius (r) = 6 cm
Height (h) = 5.77 cm

Curved Surface Area of the Cylinder:
= 2πrh
= 2 * π * 6 * 5.77
= 69.01 cm²

Surface Area of one Circular Base:
= πr²
= π * 6²
= 113.10 cm²

Since there are two circular bases, the total surface area of the pencil sharpener is calculated as follows:
Total Surface Area = Curved Surface Area + 2 * Surface Area of one Circular Base
Total Surface Area = 69.01 + 2 * 113.10
Total Surface Area = 69.01 + 226.20
Total Surface Area = 295.21 cm²

Therefore, the correct total surface area of the pencil sharpener is 295.21 cm².