What is the volume of the pyramid

Question

l(10) w(7) hight(11)

Answer 1

The volume \( V \) of a pyramid can be calculated using the formula:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

For a rectangular base, the base area is calculated as:

\[ \text{Base Area} = \text{length} \times \text{width} = l \times w \]

In your case, the dimensions of the pyramid are:

• Length (\( l \)) = 10
• Width (\( w \)) = 7
• Height (\( h \)) = 11

First, calculate the base area:

\[ \text{Base Area} = 10 \times 7 = 70 \]

Next, substitute the base area and the height into the volume formula:

\[ V = \frac{1}{3} \times 70 \times 11 \]

Calculating that gives:

\[ V = \frac{1}{3} \times 770 = \frac{770}{3} \approx 256.67 \]

Thus, the volume of the pyramid is approximately \( 256.67 \) cubic units.

Answer 2

now
l(24) w(15) h(20)

Answer 3

To find the volume of a pyramid with the new dimensions \( l = 24 \), \( w = 15 \), and \( h = 20 \), we can use the same formula for the volume of a pyramid:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

First, we calculate the base area:

\[ \text{Base Area} = l \times w = 24 \times 15 \]

Calculating that:

\[ \text{Base Area} = 360 \]

Next, substitute the base area and the height into the volume formula:

\[ V = \frac{1}{3} \times 360 \times 20 \]

Calculating that gives:

\[ V = \frac{1}{3} \times 7200 = 2400 \]

Thus, the volume of the pyramid is \( 2400 \) cubic units.

Answer 4

A right rectangular pyramid has an altitude of 22.3 inches, a length of 6.75 inches, and a width of 10.25 inches. What is the volume of the pyramid in cubic inches

Answer 5

To find the volume of a right rectangular pyramid, we can use the formula:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

For a rectangular base, the base area can be calculated as:

\[ \text{Base Area} = \text{length} \times \text{width} = l \times w \]

In your case, the dimensions of the pyramid are:

• Length (\( l \)) = 6.75 inches
• Width (\( w \)) = 10.25 inches
• Height (\( h \)) = 22.3 inches

Step 1: Calculate the Base Area

\[ \text{Base Area} = 6.75 \times 10.25 \]

Calculating that:

\[ \text{Base Area} = 69.1875 \text{ square inches} \]

Step 2: Calculate the Volume

Now substitute the base area and the height into the volume formula:

\[ V = \frac{1}{3} \times 69.1875 \times 22.3 \]

Calculating that gives:

\[ V = \frac{1}{3} \times 1547.6875 = 515.8958333 \]

Final Result

Thus, the volume of the pyramid is approximately

\[ V \approx 515.90 \text{ cubic inches.} \]

Answer 6

Leon was wondering one day what the volume of the Eiffel Tower would be if the sides were solid. The base is a square with sides measuring 125 m long on each side, and the altitude of the square pyramid is 324 m.

Answer 7

To find the volume of the Eiffel Tower, which can be approximated as a square pyramid, we can use the formula for the volume of a pyramid:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

Step 1: Calculate the Base Area

For a square base, the area is given by:

\[ \text{Base Area} = \text{length} \times \text{width} = s^2 \]

Where \( s \) is the side length of the base. Given that each side of the square base measures 125 m:

\[ \text{Base Area} = 125 \times 125 = 15625 \text{ m}^2 \]

Step 2: Substitute into the Volume Formula

Now we can substitute the base area and the height into the volume formula. The height \( h \) of the pyramid is given as 324 m:

\[ V = \frac{1}{3} \times 15625 \times 324 \]

Step 3: Calculate the Volume

Calculating:

\[ V = \frac{1}{3} \times 5062500 \]

\[ V = 1687500 \text{ m}^3 \]

Final Result

The volume of the Eiffel Tower, if the sides were solid, would be approximately

\[ V = 1687500 \text{ cubic meters.} \]

Answer 8

Cecilia built a model pyramid out of foam. Her model is 20 inches high, with a rectangular base that is 8 inches long and 12 inches wide. What is the volume of her model in cubic inches

Answer 9

To find the volume of Cecilia's model pyramid, we will use the formula for the volume of a pyramid:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

Step 1: Calculate the Base Area

For a rectangular base, the area can be calculated as:

\[ \text{Base Area} = \text{length} \times \text{width} = l \times w \]

Given that:

• Length (\( l \)) = 8 inches
• Width (\( w \)) = 12 inches

Calculating the base area:

\[ \text{Base Area} = 8 \times 12 = 96 \text{ square inches} \]

Step 2: Substitute Values into the Volume Formula

Now substitute the base area and height into the volume formula. The height (\( h \)) is given as 20 inches:

\[ V = \frac{1}{3} \times 96 \times 20 \]

Step 3: Calculate the Volume

Calculating:

\[ V = \frac{1}{3} \times 1920 = 640 \text{ cubic inches} \]

Final Result

Thus, the volume of Cecilia's model pyramid is

\[ V = 640 \text{ cubic inches.} \]