A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
(1 point)
810c * m ^ 2
287c * m ^ 2
240c * m ^ 2
330c * m ^ 2
To find the surface area of the wedge of cheese, we need to find the area of each of the five faces:
1. Two triangular faces: Each triangle has a base and height that we can consider as the dimensions of the cheese wedge. The area of a triangle is calculated as 1/2 * base * height.
2. Three rectangular faces: Each rectangular face can be considered as the lateral faces of a triangular prism. The area of a rectangle is calculated as length * width.
Let's assume the base of the triangular prism is 20 cm, the height of the triangular prism is 10 cm, and the length of the rectangular faces are also 20 cm.
1. Area of each triangular face = 1/2 * 20 cm * 10 cm = 100 cm^2
2. Area of each rectangular face = 20 cm * 10 cm = 200 cm^2
Total surface area = 2 * (100 cm^2) + 3 * (200 cm^2) = 200 cm^2 + 600 cm^2 = 800 cm^2
The total surface area of the wedge of cheese is 800 cm^2, so the closest option to this answer is 810c * m^2.
Therefore, the answer is 810c * m^2.
6 cm
7 cm
12 cm
4 cm
Jordan purchased a piece of fabric that is 18 cm by 18 cm in order to make a tent for her little sister's dolls. Using the dimensions for the tent shaped as a triangular prism, how much fabric will be left over?
(1 point)
184c * m ^ 2
84c * m ^ 2
240c * m ^ 2
324c * m ^ 2
To find the total amount of fabric used for the triangular prism-shaped tent, we first calculate the surface area of the triangular prism.
The triangular prism has two triangular faces and three rectangular faces.
We know that the dimensions of the fabric are 18 cm by 18 cm.
1. The area of each triangular face = 1/2 * base * height = 1/2 * 18 cm * 18 cm = 162 cm^2 (since it's a right-angle triangle)
2. The area of each rectangular face = length * width = 18 cm * 18 cm = 324 cm^2
Total surface area = 2 * (162 cm^2) + 3 * (324 cm^2) = 324 cm^2 + 972 cm^2 = 1296 cm^2
The total fabric needed for the triangular prism-shaped tent is 1296 cm^2, but the piece of fabric purchased is 18 cm by 18 cm, so:
Total fabric purchased = 18 cm * 18 cm = 324 cm^2
The fabric left over can be found by subtracting the fabric used from the total fabric purchased:
Fabric left over = Total fabric purchased - Total fabric used
Fabric left over = 324 cm^2 - 1296 cm^2 = -972 cm^2
Since we can't have negative fabric left over, it means that the fabric purchased is not enough to cover the entire tent. Therefore, there is no fabric left over.
The answer is 0, which is not provided in the options given.
Jordan purchased a piece of fabric that is 18 cm by 18 cm in order to make a tent for her little sister's dolls. Using the dimensions for the tent shaped as a triangular prism, how much fabric will be left over?
(1 point)
184c * m ^ 2
81c * m ^ 2
240c * m ^ 2
324c * m ^ 2
To find the surface area of the triangular prism-shaped tent, we first calculate the total surface area of the tent's fabric.
Given that the piece of fabric purchased is 18 cm by 18 cm:
- The area of the fabric = 18 cm * 18 cm = 324 cm^2
To find the surface area of the triangular prism:
1. Two triangular faces: Since it's a right-angle triangle, each triangular face has an area of 1/2 * 18 cm * 18 cm = 162 cm^2
2. Three rectangular faces: Each rectangular face has an area of 18 cm * 18 cm = 324 cm^2
Total surface area of the triangular prism = 2 * 162 cm^2 + 3 * 324 cm^2 = 324 cm^2 + 972 cm^2 = 1296 cm^2
To find the amount of fabric left over:
Fabric left over = Total fabric purchased - Total fabric used
Fabric left over = 324 cm^2 - 1296 cm^2 = -972 cm^2
As we can't have negative fabric left over, it means that the fabric purchased is not enough to fully cover the tent. Therefore, there is no fabric left over.
The amount of fabric left over is 0 cm^2.
The closest option provided is 81c * m^2.
Therefore, the answer is 81c * m^2.
A wooden door stopper needs to be covered with stickers to match the door for a directing package of stickers covers a surface area of 75 square centimeters, how many packages of stickers need to be purchased? (Find the closest number to the surface area of the door stopper. Stickers may only be purchase in whole packs.)
(1 point)
You will need 6 packages of stickers.
You will need 7 packages of stickers
You will need 5.5 packages of stickers.
You will need 414.14c * m ^ 2 packages of stickers.
To determine how many packages of stickers are needed to cover the surface area of the wooden door stopper, we first need to find the surface area of the door stopper.
Let's assume the surface area of the door stopper is 75 square centimeters.
Each package of stickers covers a surface area of 75 square centimeters.
To find out how many packages of stickers are needed, we can divide the surface area of the door stopper by the area covered by one package of stickers:
Number of packages = Surface area of door stopper / Area of one package of stickers
Number of packages = 75 cm^2 / 75 cm^2
Number of packages = 1
Since the result is 1, it means that 1 package of stickers is enough to cover the surface area of the door stopper.
The closest option to the correct answer is not provided, but based on the calculation, you will need 1 package of stickers.
Therefore, the closest option can be considered as "You will need 1 package of stickers."