The user has not provided a question for problem 3, but problems 1 and 2 are: "What is the perimeter of the…

Question

The user has not provided a question for problem 3, but problems 1 and 2 are: "What is the perimeter of the pentagon below?" and "Calculate the surface area of the rectangular prism."

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for problems 1, 2, and 3:

1. What is the perimeter of the pentagon below?

Identify the shape and its properties.
The shape is a regular pentagon, which has 5 equal sides. The length of one side is given as 3.2 cm.
Use the formula for the perimeter of a regular pentagon.
The perimeter $P$ is the sum of the lengths of all sides.
$P = \text{number of sides} \times \text{side length}$ $P = 5 \times 3.2 \text{ cm}$
Calculate the perimeter.
$P = 16.0 \text{ cm}$
The perimeter of the pentagon is:
$\boxed{16.0 \text{ cm}}$
2. Calculate the surface area of the rectangular prism.
Identify the dimensions of the rectangular prism.
Length $l = 7$ cm
Width $w = 2$ cm
Height $h = 3$ cm
Use the formula for the surface area of a rectangular prism.
$\text{Surface Area (SA)} = 2(lw + lh + wh)$
Substitute the dimensions into the formula and calculate.
$\text{SA} = 2((7 \text{ cm} \times 2 \text{ cm}) + (7 \text{ cm} \times 3 \text{ cm}) + (2 \text{ cm} \times 3 \text{ cm}))$ $\text{SA} = 2(14 \text{ cm}^2 + 21 \text{ cm}^2 + 6 \text{ cm}^2)$ $\text{SA} = 2(41 \text{ cm}^2)$ $\text{SA} = 82 \text{ cm}^2$
The surface area of the rectangular prism is:
$\boxed{82 \text{ cm}^2}$
3. Calculate surface area of the open cylinder. Use $\pi = 3.14$ .
Identify the given values and ensure consistent units.
Radius $r = 50$ cm
Height $h = 1.2$ m
Convert height to centimeters: $h = 1.2 \text{ m} \times 100 \text{ cm/m} = 120$ cm
Use $\pi = 3.14$ .
Determine the formula for the surface area of an open cylinder.
An open cylinder has one circular base and a curved surface, but no top.
$\text{Surface Area (SA)} = \text{Area of base} + \text{Area of curved surface}$ $\text{SA} = \pi r^2 + 2\pi rh$
Substitute the values into the formula.
$\text{SA} = (3.14 \times (50 \text{ cm})^2) + (2 \times 3.14 \times 50 \text{ cm} \times 120 \text{ cm})$
Calculate the area of the base.
$\text{Area of base} = 3.14 \times 2500 \text{ cm}^2 = 7850 \text{ cm}^2$
Calculate the area of the curved surface.
$\text{Area of curved surface} = 2 \times 3.14 \times 50 \times 120 \text{ cm}^2$ $\text{Area of curved surface} = 3.14 \times 100 \times 120 \text{ cm}^2$ $\text{Area of curved surface} = 3.14 \times 12000 \text{ cm}^2 = 37680 \text{ cm}^2$
Add the areas to find the total surface area.
$\text{SA} = 7850 \text{ cm}^2 + 37680 \text{ cm}^2$ $\text{SA} = 45530 \text{ cm}^2$
The surface area of the open cylinder is:
$\boxed{45530 \text{ cm}^2}$

The user has not provided a question for problem 3, but problems 1 and 2 are: "What is the perimeter of the pentagon below?" and "Calculate the surface area of the rectangular prism."

Step-by-step solution

Identify the shape and its properties.

Use the formula for the perimeter of a regular pentagon.

Calculate the perimeter.

Identify the dimensions of the rectangular prism.

Use the formula for the surface area of a rectangular prism.

Substitute the dimensions into the formula and calculate.

Identify the given values and ensure consistent units.

Determine the formula for the surface area of an open cylinder.

Substitute the values into the formula.

Calculate the area of the base.

Calculate the area of the curved surface.

Add the areas to find the total surface area.

Still stuck on this one?

More Mathematics Questions