First, we need to find the length of a side for the cube.

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

, whereis 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, because the pyramid and the cube share a base, we know that the pyramid must be a square pryamid.

Recall how to find the volume of a pyramid:

Now, since the pyramid is the same height as the cube, the height of the pyramid is also.

For any prism, the volume is given by the following equation:

The question gives us the area of the base and the height.

Start by taking a cube that is. The volume of this cube is.

Next, triple the sides of this cube so that it becomes. The volume of this cube is.

The volume of the new cube istimes as large as the original.

The fastest way to solve this problem is to plug all of the answer choices in forand look for an output of.

Alternatively, one could set the surface area formula equal to(knowing that), but this would require solving a quadratic.

Rearranging this we get

Now factoring out awe get:

Since we cannot have a negative length our answer is.

The surface area of the half cylinder will consist of the lateral area and the base area.

There are three parts to the surface area:

Rectangular region, semi-circular bases of the half cylinder, and outer face of the cylinder.

The cross section of the half cylinder is a rectangle. Find the area of the rectangle. The diameter of the semicircle represents the width of the rectangle, which is double the radius. The length of the rectangle is the height of the cylinder.

Next, find the area of a semicircular bases.

Since there are two semicircular bases of the semi-cylinder, the total area of the semicircular bases is.

Find the area of the outer region. The area of the outer region is the half circumference multiplied by the height of the cylinder.

Sum the areas of the rectangle, the two circular bases, and the outer region to find the lateral area.

There are 7.48 gallons in cubic foot. Set up a ratio:

1 ft^3./ 7.48 gallons = x cubic feet / 10,000 gallons

Pool Volume = 10,000 gallons = 10,000 gallons * (1 ft^3./ 7.48 gallons) = 1336.9 ft^3.

Pool Volume = 4ft x 10 ft x WIDTH = 1336.9 cubic feet

Solve for WIDTH:

4 ft x 10 ft x WIDTH = 1336.9 cubic feet

WIDTH = 1336.9 / (4 x 10) = 33.4 ft

多维数据集的容积是64厘米^3., making the length of one edge 4cm (4 * 4 * 4 = 64).

So the area of one side is 4 * 4 = 16cm²

The formula to find the volume of the cube is

Since we know the volume, we can set up the equation

To find the length of the side of a square given the surface area, use the surface area formula and solve for:

, now divide both sides by 6
, now square root both sides
.

To find the length of the edge of a cube from its surface area, remember that, whereis the length of a side.

So, the box isunits long.