Question

Expression for the Volume of a Hexagonal Prism and Volume of a Pyramid.

a.V hexagonal prism =xy, V pyramid=1/3 x2
b.V hexagonal prism=xy, V pyramid=1/3 x2
c.V hexagonal prism=xy, V pyramid=7x d. V hexagonal prism=x2, V pyramid=1/3xy

Answer 1

The expressions for the volumes are: V hexagonal prism = x.y, V pyramid = 1/3 x^2 h. Option a is correct.

Step-by-step explanation:

Here's why:

• Hexagonal prism: Volume is simply the area of the base (a hexagon) multiplied by the height (y). So, V = x.y, where x is the area of the hexagon.
• Pyramid: Volume is 1/3 of the area of the base (again, a hexagon) multiplied by the height (h). This formula applies to any pyramid, not just hexagonal ones. So, V = 1/3.x^2.h.

Options b, c, and d all have errors:

• b: It repeats the correct formula for the prism but uses x^2 for the pyramid, which is incorrect.
• c: It correctly uses x.y for the prism but uses a constant value (7x) for the pyramid's volume, which is impossible without knowing the base area and height.
• d: It uses x^2 for the prism, which should be x.y. Additionally, it incorrectly uses the area of the base (x^2) instead of 1/3 of it for the pyramid's volume.

Therefore, only option a accurately reflects the volume formulas for both the hexagonal prism and pyramid.

Remember, the area of the hexagon (x) needs to be determined separately for both shapes to find their final volumes.

Correct answer: option a