Question
There is a piece of cheese which is a prism. The cross section is a sector of a circle of radius 14 cm and angle 25 degree. The height of the piece of cheese is 6cm. Calculate the volume.
Answers
GPT 3.5
To calculate the volume of the prism-shaped piece of cheese, we first need to calculate the area of the circular cross-section, which is a sector of a circle with radius 14 cm and angle 25 degrees.
The area of a sector of a circle can be calculated using the formula:
\[ A = \frac{n}{360} \times \pi r^2 \]
where:
- A is the area of the sector,
- n is the angle of the sector in degrees,
- r is the radius of the circle.
Substitute the values:
\[ A = \frac{25}{360} \times \pi (14)^2 \]
\[ A = \frac{25}{360} \times \pi \times 196 \]
\[ A = \frac{25}{360} \times 615.75 \]
\[ A = 42.81 \, cm^2 \]
Now, we can calculate the volume of the prism-shaped piece of cheese by multiplying the area of the circular cross-section by the height of the piece:
\[ V = A \times h \]
\[ V = 42.81 \times 6 \]
\[ V = 256.86 \, cm^3 \]
Therefore, the volume of the prism-shaped piece of cheese is 256.86 cubic centimeters.
The area of a sector of a circle can be calculated using the formula:
\[ A = \frac{n}{360} \times \pi r^2 \]
where:
- A is the area of the sector,
- n is the angle of the sector in degrees,
- r is the radius of the circle.
Substitute the values:
\[ A = \frac{25}{360} \times \pi (14)^2 \]
\[ A = \frac{25}{360} \times \pi \times 196 \]
\[ A = \frac{25}{360} \times 615.75 \]
\[ A = 42.81 \, cm^2 \]
Now, we can calculate the volume of the prism-shaped piece of cheese by multiplying the area of the circular cross-section by the height of the piece:
\[ V = A \times h \]
\[ V = 42.81 \times 6 \]
\[ V = 256.86 \, cm^3 \]
Therefore, the volume of the prism-shaped piece of cheese is 256.86 cubic centimeters.