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.

Answer 1

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.