Convert each measurement from inches to feet by multiplying it by 12:

Height: 4 feet = $\displaystyle 4 \times 12 = 48$ inches

Sidelength of the base: 3 feet = $\displaystyle 3 \times 12 = 36$ inches

The volume of a pyramid is 

$\displaystyle V = \frac{1}{3} Bh$

Since the base is a square, we can replace $\displaystyle B = s^{2}$:

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

Substitute $\displaystyle s=36, h = 48$

$\displaystyle V = \frac{1}{3} \cdot 36 ^{2}\cdot 48$

$\displaystyle V =20,736$

The pyramid has volume 20,736 cubic inches.

In order to find the area of a triangle, we use the formula $\displaystyle \frac{1}{3}Bh$.  In this case, since the base is a square, we can replace $\displaystyle B$ with $\displaystyle s^{2}$, so our formula for volume is $\displaystyle \frac{1}{3}s^{2}h$.

Since the length of each side of the base is $\displaystyle 40$ feet, we can substitute it in for $\displaystyle s$.

$\displaystyle \frac{1}{3}\cdot (40)^{2}\cdot h$

We also know that the height is $\displaystyle 300$ feet, so we can substitute that in for $\displaystyle h$.

$\displaystyle \frac{1}{3}\cdot (40)^{2}\cdot 300$

This gives us an answer of $\displaystyle 160,000 ft^{3}$.

It is important to remember that volume is expressed in units cubed.

Convert each of the measurements from feet to inches by multiplying by $\displaystyle 12$.

Height: $\displaystyle 2 \times 12 = 24$ inches

Sidelength of base: $\displaystyle 3 \times 12 = 36$ inches

The base of the pyramid has area 

$\displaystyle B = s^{2} = 36^{2} = 1,296$ square inches.

Substitute $\displaystyle B = 1,296, h = 24$  into the volume formula:

$\displaystyle V = \frac {1}{3} Bh$

$\displaystyle V = \frac {1}{3} \cdot 1,296 \cdot 24 =10,368$ cubic inches

Convert each of the measurements from inches to feet by dividing by .

Height: $\displaystyle 42 \div 12 = 3 \frac{1}{2}$ feet

Sidelength: $\displaystyle 24 \div 12 = 2$ feet

The base of the pyramid has area 

$\displaystyle B = s^{2} = 2^{2} = 4$ square feet.

Substitute $\displaystyle B = 4, h = 3 \frac{1}{2}$  into the volume formula:

$\displaystyle V = \frac {1}{3} Bh$

$\displaystyle V = \frac {1}{3}\cdot 4 \cdot 3 \frac{1}{2}$

$\displaystyle V = \frac {1}{3} \cdot \frac {4}{1} \cdot \frac{7}{2}$

$\displaystyle V = \frac {1}{3} \cdot \frac {2}{1} \cdot \frac{7}{1} = \frac {14}{3} = 4 \frac {2}{3}$ cubic feet

The perimeter of the square base, $\displaystyle 3$ feet, is equivalent to $\displaystyle 3 \times 12 = 36$ inches; divide by $\displaystyle 4$ to get the sidelength of the base - and the height: $\displaystyle 36 \div 4 = 9$ inches. 

The area of the base is therefore $\displaystyle B = s^{2} = 9^{2} = 81$ square inches. 

In the formula for the volume of a pyramid, substitute $\displaystyle B = 81,h=9$:

$\displaystyle V = \frac{1}{3} Bh = \frac{1}{3}\cdot 81 \cdot 9 = 243$ cubic inches.

The volume of a pyramid can be determined using the following equation:

$\displaystyle V=\frac{1}{3}lwh=\frac{1}{3}(7)(6)(9)=126$

The pyramid has a square base that is $\displaystyle n$ units by $\displaystyle n$ units, and its height is $\displaystyle n$ units, as can be seen from this diagram,

The square base has area $\displaystyle B = n^{2}$; the pyramid has volume $\displaystyle V = \frac{1}{3} \cdot n^{2} \cdot n = \frac{1}{3} n^{3}$

Since the volume is 1,000, we can set this equal to 1,000 and solve for $\displaystyle n$:

$\displaystyle \frac{1}{3} n^{3} = 1,000$

$\displaystyle n^{3} = 3,000$

$\displaystyle n = \sqrt[3]{3,000} = \sqrt[3]{1,000} \cdot \sqrt[3]{3 } = 10 \sqrt[3]{3 }$

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

$\displaystyle V = \frac{l \cdot w \cdot h}{3}$

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

Now, we know the base of the pyramid has a length of 4in.  We also know the base of the pyramid has a width of 3in.  We also know the pyramid has a height of 5in. 

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

$\displaystyle V = \frac{4\text{in} \cdot 3\text{in} \cdot 5\text{in}}{3}$

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

$\displaystyle V = 20\text{in}^3$

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

$\displaystyle V = \frac{l \cdot w \cdot h}{3}$

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

Now, we know the following measurements:

• length = 4cm
• width = 9cm
• height = 8cm

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

$\displaystyle V = \frac{4\text{cm} \cdot 9\text{cm} \cdot 8\text{cm}}{3}$

$\displaystyle V = \frac{288\text{cm}^3}{3}$

$\displaystyle V = 96\text{cm}^3$

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

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

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

Now, we know the following measurements:

• length:  7in
• width:  6in
• height:  8in

So, we get

$\displaystyle V = \frac{ 7\text{in} \cdot 6\text{in} \cdot 8\text{in}}{3}$

$\displaystyle V = \frac{42\text{in}^2 \cdot 8\text{in}}{3}$

$\displaystyle V = \frac{336\text{in}^3}{3}$

$\displaystyle V = 112\text{in}^3$