Question

If the base of a prism is a regular hexagon of side 6 cm and the height is 10 cm, what is its volume?

• A. 550√2 cm³
• B. 500√6 cm³
• C. 480√3 cm³
• D. 540√3 cm³

Answer 1

Answer:

D. 540√3 cm³

Volume of a prism = area of base × height

Area of regular hexagon

A regular hexagon can be split into 6 equilateral triangles of side 6 cm.

Area of one equilateral triangle:
$\frac{\sqrt{3}}{4}a^2 = \frac{\sqrt{3}}{4} \times 6^2 = \frac{\sqrt{3}}{4} \times 36 = 9\sqrt{3}$

So, area of hexagon:

$6 \times 9\sqrt{3} = 54\sqrt{3} \text{ cm}^2$

Step 2: Volume of prism

Height = 10 cm

$V = 54\sqrt{3} \times 10 = 540\sqrt{3}4$

Step 3: Approximate value

$\sqrt{3} \approx 1.732$
$V \approx 540 \times 1.732 = 935.28$

Final Answer:

$\boxed{540\sqrt{3} } {cm}^3$