Question

Find the diameter of a cone whose volume and height are 3696 cubic units and 18 units, respectively. (π=22/7)

• A. 28 units
• B. 36 units
• C. 26 units
• D. 38 units

Answer 1

Answer:

A. 28 units

The diameter of the cone is 28 units.

• Volume ($V$): 3,696 cubic units

• Height ($h$): 18 units

• $\pi$: $\frac{22}{7}$

Step 1: Write down the volume formula for a cone
$V = \frac{1}{3} \pi r^2 h$

Step 2: Substitute the known values to find the radius ($r$)
$3696 = \frac{1}{3} \times \frac{22}{7} \times r^2 \times 18$

Simplify by dividing 18 by 3:
$3696 = \frac{22}{7} \times r^2 \times 6$
$3696 = \frac{132}{7} \times r^2$

Step 3: Solve for $r^2$
$r^2 = \frac{3696 \times 7}{132}$
$r^2 = 28 \times 7$
$r^2 = 196$
$r = \sqrt{196} = 14\text{ units}$

Step 4: Calculate the diameter ($d$)
$\text{Diameter} = 2 \times r$
$\text{Diameter} = 2 \times 14 = 28\text{ units}$