A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese? the demission's of the cheese is 12cm 5cm 9cm 13cm
The answer choices are
287 cm2
330 cm2
810 cm2
240cm2
To find the total surface area of the cheese, we need to find the area of each face and add them up.
There are three rectangular faces, each with an area of length times width:
- Face 1: 12 cm x 5 cm = 60 cm2
- Face 2: 9 cm x 5 cm = 45 cm2
- Face 3: 13 cm x 5 cm = 65 cm2
There are also two triangular faces. To find the area of a triangle, we use the formula (base x height)/2.
- Face 4: (12 cm x 9 cm)/2 = 54 cm2
- Face 5: (13 cm x 9 cm)/2 = 58.5 cm2
Adding up all the areas, we get:
60 cm2 + 45 cm2 + 65 cm2 + 54 cm2 + 58.5 cm2 = 282.5 cm2
Rounding to the nearest whole number, the closest answer choice is 287 cm2. Therefore, the answer is 287 cm2.
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
A party store offers small balloons and large balloons. You can choose from pink, blue, green, and yellow balloons. You can choose from silver, gold, and white ribbons. Use the counting principle to find the number of different ways you can choose a balloon with a ribbon.
To use the counting principle, we need to multiply the number of options for choosing the balloon by the number of options for choosing the ribbon.
There are 2 sizes of balloons (small and large) and 4 colors of balloons (pink, blue, green, and yellow). So there are:
2 options for the size of balloon x 4 options for the color of balloon = 8 options for choosing a balloon
There are 3 options for the color of ribbon (silver, gold, white).
So using the counting principle, the total number of different ways we can choose a balloon with a ribbon is:
8 options for choosing a balloon x 3 options for choosing a ribbon = 24 different ways
Therefore, there are 24 different ways you can choose a balloon with a ribbon.
To find the amount of plastic wrap needed to cover the wedge of cheese, we need to calculate the surface area of the triangular prism.
The triangular prism has three rectangular faces and two triangular faces. Let's calculate the surface area step by step:
1. Calculate the surface area of the rectangular faces:
The wedge of cheese has two identical rectangular faces with dimensions 12cm x 5cm and two identical rectangular faces with dimensions 9cm x 5cm.
The total surface area of the rectangular faces can be calculated as follows:
2(Length x Width) + 2(Length x Height) + 2(Width x Height)
= 2(12cm x 5cm) + 2(9cm x 5cm) + 2(12cm x 9cm)
= 120cm² + 90cm² + 216cm²
= 426cm²
2. Calculate the surface area of the triangular faces:
The two triangular faces of the wedge of cheese are identical and have base and height dimensions of 12cm and 13cm, respectively.
The formula for the area of a triangle is 1/2(base x height).
Therefore, the area of each triangular face is:
1/2(12cm x 13cm) = 78cm²
3. Total surface area:
The total surface area of the wedge of cheese is the sum of the surface area of the rectangular faces and the surface area of the triangular faces:
Total surface area = Surface area of rectangular faces + Surface area of triangular faces
= 426cm² + 2(78cm²)
= 426cm² + 156cm²
= 582cm²
Therefore, the amount of plastic wrap needed to cover the wedge of cheese is 582cm².
From the given answer choices, the closest option to 582cm² is 810cm².