The volume of a triangular prism can be simply stated as V = A*L, where A is the area of the triangular face and L is the length. We have the volume already and we need to figure out the area of the triangle from the side length.

The area of a triangle is b*h/2, and we are given the base/side length: 3 in. We also have a formula for the height of an equilateral triangle, . Calculating the area of the triangle we get 2.5981 in^2, so now we just have to plug our numbers into the volume formula.

And that is the final answer.

First, find the volume of the pool. For a rectangular prism, the formula for the volume is the following:

For the swimming pool,

 cubic meters

Now, because the hose only fills up  cubic meters per hour, divide the total volume by  to find how long it will take for the pool to fill.

It will take the pool  hours to fill by hose.

First, find the volume of the cake. For a rectangular prism,

Next, find the volume of each individual slice.

Now, divide the volume of the entire cake by the volume of the slice to get how many pieces of cake Matt can cut.

First, find the side lengths of the cube.

Recall that the surface area of the cube is given by the following equation:

, where  is the length of a side.

Plugging in the surface area given by the equation, we can then find the side length of the cube.

Now, recall that the volume of a cube is given by the following equation:

The volume of a right triangular prism is given by the following equation:

Now, for the given question, the height is .

Since the area of the base is a right triangle, we can plug in the given values to find .

The volume of a right triangular prism is given by the following equation:

For a rectangular prism, the formula for the volume is the following:

Now, we know that the height is twice its width. We can rewrite that as:

We also know that the height is half its length. That can be written as:

Now, we can plug in the values of the length, width, and height in terms of height to find the height.

The question wants to find the length of the box. Plug in the value of the height in the earlier equation we wrote earlier to represent the relatioinship between the height and the length.

First, we will need to find the length of a side of the tetrahedron.

We can use the surface area to find the lengh of a side. Recall that the formula to find the surface of a tetrahedron:

, where  is the side length.

Now, recall the formula to find the volume of a tetrahedron:

The volume of a right triangular prism is given by the following equation:

First, find the volume of the die. For a cube, the volume has the following formula:

Because it costs  for each cubic centimeter, you will need to multiply this number by  to get the cost of each die.