Start by finding the volume of the rectangular prism.

\(\displaystyle \text{Volume}=\text{length}\times \text{width}\times \text{height}\)

For the given dimensions,

\(\displaystyle \text{Volume}=12\times 16 \times 30=5760\)

Since Tammy needs to remove two-thirds of the water, we will need to find two-thirds of the volume.

\(\displaystyle (5760)\frac{2}{3}=3840\)

Tammy must remove \(\displaystyle 3840in^3\) of water.

Write the formula for the area of a rectangular solid.

\(\displaystyle V =LWH\)

The base area consists of \(\displaystyle LW\), which means we can substitute the area as replacement of the two variables.

\(\displaystyle V =LWH = (4)(5) = 20\)

The answer is:  \(\displaystyle 20\)

Since Amy is painting the outside of a box, we will need to find the surface area of the box.

Recall how to find the surface area of a rectangular prism:

\(\displaystyle \text{Surface Area}=2(wl+hl+hw)\), where \(\displaystyle w\) is the width, \(\displaystyle h\) is the height, and \(\displaystyle l\) is the length.

Because we are only interested in the amount of blue paint that Amy will be painting, we know that we will need to find one-third of the surface area.

\(\displaystyle \text{Area of Blue Paint}=\frac{\text{Surface Area}}{3}=\frac{2(wl+hl+hw)}{3}\)

Plug in the dimensions of the box to find the area of the blue paint.

\(\displaystyle \text{Area of Blue Paint}=\frac{2((4)(6)+(6)(10)+(4)(10))}{3}=\frac{248}{3}=82.67\)

The volume of a rectangular prism is equal to the product of its three dimensions, so here,

\(\displaystyle V= x \cdot 2x \cdot (x+6)\)

\(\displaystyle =2 \cdot x \cdot x \cdot (x+6)\)

\(\displaystyle =2 x ^{2} (x+6)\)

Apply the distribution property, multiplying \(\displaystyle 2x^{2}\) by each of the expressions in the parentheses:

\(\displaystyle V =2 x ^{2} \cdot x+2 x ^{2} \cdot 6\)

\(\displaystyle =2 x ^{2+1} +2 \cdot 6 \cdot x ^{2}\)

\(\displaystyle =2 x ^{3} +12 x ^{2}\)

You are building a metal crate to hold fishing equipment. If the crate will be 1.5 ft long, 2 feet tall, and 5 feet wide, what will its volume be?

We are asked to find the volume of a rectangular solid. In this case it is a metal crate, but it is essentially a rectangular solid. To find its volume, use the following formula:

\(\displaystyle V=l*w*h\)

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

\(\displaystyle V=1.5ft*2ft*5ft=1.5ft*10ft^2=15ft^3\)

\(\displaystyle V=15ft^3\)

First, convert the dimensions of the prism to centimeters. One meter is equal to 100 centimeters, so multiply by this conversion factor:

\(\displaystyle 0.8 \textup{ m } \times 100 \textup{ cm /m} = 80 \textup{ cm}\)

\(\displaystyle 0.3 \textup{ m } \times 100 \textup{ cm /m} =30 \textup{ cm}\)

The dimensions of the prism are 80 centimeters by 30 centimeters by centimeters; multiply these dimensions to find the volume:

\(\displaystyle V = 80 \textup{ cm} \times 30 \textup{ cm} \times 30 \textup{ cm}\)

\(\displaystyle = 72,000 \textup{ cm}^{3}\)

Using the given mass of 7.9 grams per cubic centimeter, multiply:

\(\displaystyle M = 72,000 \textup{ cm}^{3} \times 7.9 \textup{ g / cm}^{3} = 568,800 \textup{ g}\)

One kilogram is equal to 1,000 grams, so divide by this conversion factor:

\(\displaystyle M = 568,800 \textup{ g} \div 1,000 \textup{ g / kg} = 568.8 \textup{ kg}\),

the correct mass of the prism.

Find the volume of a rectangular prism with the following dimensions: 6 ft by 12 ft by 4 ft.

To find the volume of a rectangular prism, simply multiply the length by the width by the height.

\(\displaystyle V=l*w*h\)

So, plug in and multiply to get:

\(\displaystyle V=6ft*4ft*12ft=24ft^2*12ft=288ft^3\)

So, our answer is:

\(\displaystyle 288 ft^3\)

Coincidentally the same as our surface area

The equation for the volume of a rectangular prism is

\(\displaystyle V=l\cdot w \cdot h\)

So we simply input our dimensions

\(\displaystyle V=5\cdot2\cdot3=30\)