Question

I need the volume for 9,11, and 13.

Answer 1

Question 1

Let's use 3.14 for pi during this.

The volume for a cone is $\pi r^{2}\dfrac{h}{3}$.

The diameter of this cone is 17.6 inches. Since the radius is half the diameter, we can find the radius by dividing this amount by 2.

17.6 ÷ 2 = 8.8

The height of this cone is 23.4 inches.

Plug the values into the equation.

$\pi\times8.8^{2}\times\dfrac{23.4}{3}$

Next, square 6.8 and divide 23.4 by 3. Also, replace the pi symbol with 3.14.

$3.14\times77.44\times7.8$

Multiply the numbers together.

The volume of this cone is approximately 1896.66 cubic inches.

Question 2

Finding the volume of a trapezoidal prism can be done by finding the are of the trapezoidal face and multiplying it by the depth.

Formula for finding the area of a trapezoid is $a = \dfrac{1}{2} h(b_{1} +b_{2} )$

The two bases are 10 and 34, and the height is 24.7 feet. Put these values into the equation.

$a = \dfrac{1}{2}\times24.7(10+34)$

Add 10 and 34, then multiply it by 24.7 and 1/2.

a = 543.4

Multiply that value by 19, which is the depth of the figure.

The volume of the prism is 10324.6 cubic feet.

Question 3

The formula for volume of a triangular pyramid is v = 1/3ah, with a the area of the base and h the height.

The formula for the area of an equilateral triangle, which is the base, is $a=\dfrac{\sqrt{3}}{4}s^{2}$

The length of the side is 12, so we can square that to get 144.

Now multiply that by $\dfrac{\sqrt{3}}{4}$ to get the area of the base.

The area of the base is about 62.35 square meters.

The height of the pyramid is 20 meters. Plug that and the area of the base into the equation.

v = 1/3 $\times$ 62.35 $\times$ 20

Multiply the numbers together to get the volume.

The volume of the pyramid is approximately 415.67 cubic meters.