Question

a cone and a triangular pyramid have a height of 9.3 m and their cross - sectional areas are equal at every level parallel to their respective bases. what is the height, x, of the triangle base of the pyramid? round to the nearest tenth. x = \square in.

Explanation:

Step1: Find cone base area

The cone has a base diameter of 6 in, so radius $r = \frac{6}{2} = 3$ in. The area of a circle is $\pi r^2$.
$\text{Area of cone base} = \pi (3)^2 = 9\pi \approx 28.2743$ in²

Step2: Set equal to triangle area

The triangular pyramid's base is a triangle with base 3.3 in and height $x$. The area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$. Set this equal to the cone's base area (since cross-sectional areas are equal at all levels, starting with the base).
$9\pi = \frac{1}{2} \times 3.3 \times x$

Step3: Solve for x

Rearrange the equation to isolate $x$.
$x = \frac{2 \times 9\pi}{3.3} = \frac{18\pi}{3.3}$
Calculate the value:
$x \approx \frac{56.5487}{3.3} \approx 17.1$

Answer:

$17.1$ in.