Use the volume formula to determine the length of the base of a pyramid that has a volume of 585 cm3

Question

585

cm
3
, a width of 15 cm, and an altitude of 9 cm.(1 point)
Responses

13 cm
13 cm

405 com
405 com

4.3 cm
4.3 cm

135 cm

Answer 1

To determine the length of the base of the pyramid, we can use the formula for the volume of a pyramid:

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

The base area of the pyramid can be calculated as:

\[ \text{Base Area} = \text{Length} \times \text{Width} \]

In this case, let \( L \) be the length of the base and we know the width is \( 15 , \text{cm} \) and the height (altitude) is \( 9 , \text{cm} \). The volume \( V \) is given as \( 585 , \text{cm}^3 \).

Substituting into the volume formula:

\[ 585 = \frac{1}{3} \times (L \times 15) \times 9 \]

First, simplify the equation:

\[ 585 = \frac{1}{3} \times 15 \times 9 \times L \]

Calculating \( \frac{1}{3} \times 15 \times 9 \):

\[ \frac{1}{3} \times 15 = 5 \] \[ 5 \times 9 = 45 \]

So the equation now is:

\[ 585 = 45L \]

Next, solve for \( L \):

\[ L = \frac{585}{45} \]

Now, perform the division:

\[ L = 13 \]

Thus, the length of the base of the pyramid is \( 13 , \text{cm} \).

The correct response is:

13 cm.

Answer 2

J Juice brand wants to create a new bottle for their products. Their marketing department wants to design a pyramid–shaped bottle with a base that is 8 cm by 15 cm, and has an altitude of 22 cm. How much juice will this new bottle hold?(1 point)
Responses

15 cm3
15

cm
3
15 cm cubed

880 cm3
880

cm
3
880 cm cubed

7,920 cm3
7
,
920

cm
3
7,920 cm cubed

2,640 cm3

Answer 3

To determine how much juice the pyramid-shaped bottle will hold, we can use the volume formula for a pyramid:

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

First, we need to calculate the base area of the pyramid. The base is a rectangle with dimensions \( 8 , \text{cm} \) and \( 15 , \text{cm} \):

\[ \text{Base Area} = \text{Length} \times \text{Width} = 8 , \text{cm} \times 15 , \text{cm} = 120 , \text{cm}^2 \]

Next, we know the height (altitude) of the pyramid is \( 22 , \text{cm} \).

Now we can use the volume formula:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} = \frac{1}{3} \times 120 , \text{cm}^2 \times 22 , \text{cm} \]

Calculating this:

\[ V = \frac{1}{3} \times 120 \times 22 \] \[ = \frac{1}{3} \times 2640 \] \[ = 880 , \text{cm}^3 \]

Thus, the bottle will hold 880 cm³ of juice.

The correct response is:

880 cm³.

Answer 4

A construction company is digging a drainage trench. It makes the shape of an upside-down rectangular pyramid. The top opening will be 30 ft. wide by 250 ft. long, and the deepest part in the middle will be 15 ft. What is the capacity for this trench?(1 point)
Responses

112,500 ft.3
112
,
500

ft
.
3
112,500 feet cubed

37,500 ft.3
37
,
500

ft
.
3
37,500 feet cubed

98.33 ft.3
98.33

ft
.
3
98.33 feet cubed

337,500 ft.3

Answer 5

To find the capacity (volume) of the upside-down rectangular pyramid-shaped trench, we can use the volume formula for a pyramid:

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

In this case, the base area is the area of the opening at the top, which is a rectangle with a width of \( 30 , \text{ft} \) and a length of \( 250 , \text{ft} \). The height (or depth) of the pyramid is \( 15 , \text{ft} \).

First, we calculate the base area:

\[ \text{Base Area} = \text{Width} \times \text{Length} = 30 , \text{ft} \times 250 , \text{ft} = 7500 , \text{ft}^2 \]

Next, we use this base area to calculate the volume:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} = \frac{1}{3} \times 7500 , \text{ft}^2 \times 15 , \text{ft} \]

Calculating this:

\[ V = \frac{1}{3} \times 7500 \times 15 \]

First, calculate \( 7500 \times 15 \):

\[ 7500 \times 15 = 112500 \]

Now, we divide by 3:

\[ V = \frac{112500}{3} = 37500 , \text{ft}^3 \]

Thus, the capacity for the trench is 37,500 ft³.

The correct response is:

37,500 ft³.

Answer 6

Use the volume formula for a rectangular pyramid to find the missing length. Damon is building a new statue in the shape of a rectangular pyramid. It needs to be 3 feet tall, 4 feet wide, and have a volume of 32 cubic feet. How long does the pyramid statue need to be?(1 point)
Responses

8 feet
8 feet

32 feet
32 feet

384 feet
384 feet

96 feet
96 feet

Answer 7

To find the missing length of the rectangular pyramid, we will use the volume formula for a pyramid:

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

For a rectangular pyramid, the base area \( A \) is given by:

\[ \text{Base Area} = \text{Length} \times \text{Width} \]

In this case, we know:

• Volume \( V = 32 , \text{ft}^3 \)
• Height \( H = 3 , \text{ft} \)
• Width \( W = 4 , \text{ft} \)

Let's denote the length of the base as \( L \). Substituting into the volume formula gives us:

\[ 32 = \frac{1}{3} \times (L \times 4) \times 3 \]

First, simplify the equation:

\[ 32 = \frac{1}{3} \times 12L \]

This simplifies to:

\[ 32 = 4L \]

Next, solve for \( L \):

\[ L = \frac{32}{4} = 8 \]

Thus, the length of the pyramid statue needs to be 8 feet.

The correct response is:

8 feet.