Write the volume formula for the pyramid.

$\displaystyle V=\frac{LWH}{3}$

Substitute the dimensions.

$\displaystyle V=\frac{2\times 5 \times 12}{3} = (2)(5)(4) = 40$

The answer is:  $\displaystyle 40$

The pool can be looked at as a trapezoidal prism with "height" 35 feet and its bases the following shape (depth exaggerated):

The area of this trapezoidal base, which has height 50 feet and bases 3 feet and 8 feet, is

$\displaystyle B = \frac{1}{2} (3+8) \cdot 50 = 275$ square feet;

The volume of the pool is the base multiplied by the "height", or 

$\displaystyle 275 \cdot 35 = 9,625$ cubic feet, the capacity of the pool.

The volume of a right circular cone of height $\displaystyle h$ and base with radius $\displaystyle r$ is 

$\displaystyle V = \frac{1}{3} \pi r^{2}h$.

The radius is 50. To find the height, we need to use the Pythagorean Theorem with the radius 50 as one leg and the slant height 130 as the hypotenuse of a right triangle, and the height $\displaystyle h$ as the other leg:

$\displaystyle h^{2} + 50^{2} = 130 ^{2}$

$\displaystyle h^{2} + 2,500= 16,900$

$\displaystyle h^{2} + 2,500- 2,500= 16,9 00 - 2,500$

$\displaystyle h^{2} = 14,4 00$

$\displaystyle h = \sqrt{14,400} = 120$

Substitute 120 for $\displaystyle h$ and 50 for $\displaystyle r$ in the volume formula:

$\displaystyle V = \frac{1}{3} \pi r^{2}h$

$\displaystyle V = \frac{1}{3} \times 3.14 \times 50^{2} \times 120$

$\displaystyle V = \frac{1}{3} \times 3.14 \times 2,500 \times 120 \approx 314,159$ cubic centimeters.

To find the volume of a cube, we will use the following formula:

$\displaystyle V = l \cdot w \cdot h$

where l is the length, w is the width, and h is the height of the cube. 

Now, we know the height of the cube is 12cm. Because it is a cube, all sides (lengths, widths, heights) are equal. Therefore, the length and the width are also 12cm. So, we can substitute. We get

$\displaystyle V = 12\text{cm} \cdot12\text{cm} \cdot12\text{cm}$

$\displaystyle V = 144\text{cm}^2 \cdot 12\text{cm}$

$\displaystyle V = 1728\text{cm}^3$

To find the volume of a cone, we will use the following formula:

$\displaystyle V = \pi r^2 \frac{h}{3}$

where r is the radius and h is the height of the cone.

Now, we know the diameter of the cone is 10in. We also know the diameter is two times the radius. Therefore, the radius is 5in.

We know the height of the cone is 6in.

Knowing all of this, we can substitute into the formula. We get

$\displaystyle V = \pi \cdot (5\text{in})^2 \cdot \frac{6\text{in}}{3}$

$\displaystyle V = \pi \cdot 25\text{in}^2 \cdot 2\text{in}$

$\displaystyle V = \pi \cdot 50\text{in}^3$

$\displaystyle V = 50\pi \text{ in}^3$

To find the volume of a cube, we will use the following formula:

$\displaystyle V = l \cdot w \cdot h$

where l is the length, w is the width, and h is the height of the cube.

Now, we know the height of the cube is 11in. Because it is a cube, all sides are equal. Therefore, the width and the length are also 11in. So, we can substitute. We get

$\displaystyle V = 11\text{in} \cdot11\text{in} \cdot11\text{in}$

$\displaystyle V = 121\text{in}^2 \cdot 11\text{in}$

$\displaystyle V = 1331\text{in}^3$

To find the volume of a cube, we will use the following formula:

$\displaystyle V = l \cdot w \cdot h$

where l is the length, w is the width, and h is the height of the cube.

Now, we know the height of the cube is 10cm. Because it is a cube, all sides (lengths, widths, heights) are equal. Therefore, the length and the width are also 10cm. So, we can substitute. We get

$\displaystyle V = 10\text{cm} \cdot 10\text{cm} \cdot 10\text{cm}$

$\displaystyle V = 100\text{cm}^2 \cdot 10\text{cm}$

$\displaystyle V = 1000\text{cm}^3$

To find the volume of a cone, we will use the following formula:

$\displaystyle V = \pi r^2 \frac{h}{3}$

where r is the radius and h is the height of the cone.

Now, we know the diameter of the cone is 8in. We also know the diameter is two times the radius. Therefore, the radius is 4in.

We know the height of the cone is 9in.

Knowing all of this, we can substitute into the formula. We get

$\displaystyle V = \pi \cdot (4\text{in})^2 \cdot \frac{9\text{in}}{3}$

$\displaystyle V = \pi \cdot 16\text{in}^2 \cdot 3\text{in}$

$\displaystyle V = \pi \cdot 48\text{in}^3$

$\displaystyle V = 48\pi \text{ in}^3$

To find the volume of a cube, we will use the following formula:

$\displaystyle V = l \cdot w \cdot h$

where l is the length, w is the width, and h is the height of the cube.

Now, we know the height of the cube is 7in. Because it is a cube, all sides are equal. Therefore, the width and the length are also 7in. So, we can substitute. We get

$\displaystyle V = 7\text{in} \cdot 7\text{in} \cdot 7\text{in}$

$\displaystyle V = 49\text{in}^2 \cdot 7\text{in}$

$\displaystyle V = 343\text{in}^3$

To find the volume of a cone, we will use the following formula:

$\displaystyle V = \pi r^2 \frac{h}{3}$

where r is the radius and h is the height of the cone.

We know $\displaystyle \pi=3.14$.

We know the diameter of the cone is 12in. We know the diameter is two times the radius. So, the radius is 6in.

We know the height is 5in.

Now, we can substitute. We get

$\displaystyle V = 3.14 \cdot (6\text{in})^2 \cdot \frac{5\text{in}}{3}$

$\displaystyle V = 3.14 \cdot 36\text{in}^2 \cdot \frac{5\text{in}}{3}$

Now, we can simplify to make things easier. The 36 and the 3 can both be divided by 3. So, we get

$\displaystyle V = 3.14 \cdot 12\text{in}^2 \cdot \frac{5\text{in}}{1}$

$\displaystyle V = 3.14 \cdot 12\text{in}^2 \cdot 5\text{in}$

$\displaystyle V = 3.14 \cdot 60\text{in}^3$

$\displaystyle V = 188.4\text{in}^3$