The area of a triangle can be calculated using the formula $\displaystyle Area = \frac{1}{2}(Base)(Height)$. Note that the height of any triangle is a perpendicular line between the base and its opposite angle; in a right triangle that's very convenient, because the right angle gives you that perpendicular relationship between two sides. So you can use 24 as the base and 7 as the height here.  That means that the area is:

$\displaystyle Area =\frac{1}{2}(24)(7)=84$

A perfect cube has square faces; if a face has perimeter $\displaystyle 8.4$ meters, then each side of each face measures one fourth of this, or $\displaystyle 2.1$ meters. The volume of the tank is the cube of this, or

$\displaystyle 2.1^{3} = 9.261$ cubic meters.

Its capacity in liters is $\displaystyle 9.261 \times 1,000 = 9,261$ liters.

$\displaystyle 90\%$ of this is 

$\displaystyle 9,261 \times 0.9 = 8,335$ liters. 

This rounds to$\displaystyle 8\textup,300$ liters, the correct response.

In order to solve this problem, we need to recall the volume formula for a rectangular prism:

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

Now that we have the correct formula, we can substitute in our known values and solve: 

$\displaystyle V=9\times4\times4$

$\displaystyle V=144\textup{ in}^3$

In order to solve this problem, we need to recall the volume formula for a rectangular prism:

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

Now that we have the correct formula, we can substitute in our known values and solve: 

$\displaystyle V=12\times5\times3$

$\displaystyle V=180\textup{ in}^3$

In order to solve this problem, we need to recall the volume formula for a rectangular prism:

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

Now that we have the correct formula, we can substitute in our known values and solve: 

$\displaystyle V=10\times4\times6$

$\displaystyle V=240\textup{ in}^3$

Given that the dimensions are: $\displaystyle 6.3 \:cm$, $\displaystyle 6.3 \:cm$, and $\displaystyle 2.1 \:cm$ and that the volume of a rectangular prism can be given by the equation:

$\displaystyle v=l \cdot w \cdot h$, where $\displaystyle l$ is length, $\displaystyle w$ is width, and $\displaystyle h$ is height, the volume can be simply solved for by substituting in the values.

$\displaystyle V = (6.3)(6.3)(2.1)$

$\displaystyle V = (39.69)(2.1)$

$\displaystyle V = 83.349\:cm^3$

This final value can be approximated to $\displaystyle 83.3\:cm^3$.

The volume of the rectangle 

$\displaystyle V = l*w*h$ 

so we plug in our values and obtain

$\displaystyle V = 4*3*8$

$\displaystyle V = 96 m^3$.

The volume of B is 7920 in³. The volume of A is 7722 in³. Treasure Chest B can hold more treasure.

A rectangular prism has a width of 3 inches, a length of 6 inches, and a height triple its length. Find the volume of the prism.

Find the volume of a rectangular prism via the following:

$\displaystyle V=l*w*h$

Where l, w, and h are the length width and height, respectively. 

We know our length and width, and we are told that our height is triple the length, so...

$\displaystyle h=3l=3*6in=18in$

Now that we have all our measurements, plug them in and solve:

$\displaystyle V=3in*6in*18in=324in^3$

A square has four sides of equal length, as seen in the diagram below.

The volume of the solid is equal to the product of its length, width, and height, as follows:

$\displaystyle V = 15 \cdot 15 \cdot x =225 x$.