Use a net to find the surface area of the prism.
A rectangular prism has a length of 15 inches, width of 6 inches, and height of 8 inches.
A. 576 in.2
B. 258 in.2
C. 516 in.2
D. 720 in.2
First, we need to draw a net of the rectangular prism.
One way to do this is to draw the six faces (sides) of the prism and then cut them out and fold them to create the shape:
```
___
/___/| /|----|\
| | | | | |
| | | | | |
6 | | 15 | | | | <-- front view
| | _____|/ |/
| | /___/| /|\
|_____| | | | | |
8 | | | | |
|_____| |/ \| <-- top view
6 15
```
From this net, we can see that there are three pairs of identical rectangular faces: one on the top and bottom, one on the front and back, and one on the left and right. Each of these faces has an area equal to its length times its width.
The surface area of the prism is the sum of the areas of all six faces. So, we can find the surface area by adding up the areas of one pair of identical faces (which we'll multiply by 2 since there are two pairs) and then adding the area of the third face.
Area of one pair of identical faces = 2(length x width) = 2(15 x 6) = 180
Area of third face = height x width = 8 x 6 = 48
Surface area = 2(180) + 48 = 360 + 48 = 408
Therefore, the surface area of the prism is 408 square inches. None of the given answer choices matches this exact value, but the closest one is C. 516 in.2.
Find the surface area of the cylinder to the nearest tenth of a square unit. Use 3.14 for π.
A cylinder is shown with a height of 9.1 inches and a radius of 4.6 inches.
A. 131.4 in.2
B. 604.6 in.2
C. 395.8 in.2
D. 291.8 in.2
The formula for the surface area of a cylinder is:
SA = 2πr^2 + 2πrh
where r is the radius of the base, h is the height, and π is approximately 3.14.
We are given that the cylinder has a height of 9.1 inches and a radius of 4.6 inches, so we can substitute those values into the formula:
SA = 2π(4.6)^2 + 2π(4.6)(9.1)
SA = 2π(21.16) + 2π(41.86)
SA = 133.08 + 263.98
SA = 397.06
Rounding to the nearest tenth, the surface area of the cylinder is approximately 397.1 square inches.
Therefore, the answer is not listed among the choices.
To find the surface area of a prism, we need to calculate the areas of all its faces and then sum them up.
In this case, the rectangular prism has the following faces:
1. The top face, which has an area equal to the length times the width: 15 inches × 6 inches = 90 square inches.
2. The bottom face, which also has the same area as the top face: 90 square inches.
3. The front face, which has an area equal to the length times the height: 15 inches × 8 inches = 120 square inches.
4. The back face, which has the same area as the front face: 120 square inches.
5. The left side face, which has an area equal to the width times the height: 6 inches × 8 inches = 48 square inches.
6. The right side face, which has the same area as the left side face: 48 square inches.
To find the total surface area, we add up the areas of all the faces:
90 + 90 + 120 + 120 + 48 + 48 = 516 square inches.
Therefore, the correct answer is C. 516 in.2.