What is the volume of a rectangular pyramid with a length of 32 cm, a width of 25 cm, and an altitude of 41 cm?(1 point)
Responses
32,800 cm3
32,800 cm cubed
98,400 cm3
98,400 cm cubed
10,933.33 cm3
10,933.33 cm cubed
32.67 cm3
The volume of a rectangular pyramid can be calculated using the formula: V = (1/3) * l * w * h, where l is the length, w is the width, and h is the altitude.
Plugging in the values, we get: V = (1/3) * 32 cm * 25 cm * 41 cm
Calculating this expression, we get: V = 32,800 cm^3
Therefore, the correct answer is: 32,800 cm3
A resort is building a scuba diving lagoon in the shape of an upside down pyramid. The top of the lagoon is a rectangle that is 50 feet by 20 feet, and the deepest point of the lagoon is in the middle at 25 feet deep. How much water does the lagoon hold?(1 point)
Responses
8,333.33 ft.3
8,333.33 feet cubed
95 ft.3
95 feet cubed
25,000 ft.3
25,000 feet cubed
75,000 ft.3
To find the volume of the upside down pyramid-shaped lagoon, we can calculate the volume of a rectangular pyramid using the formula: V = (1/3) * b * l * h, where b is the base length, l is the base width, and h is the height.
In this case, the base length (b) is 50 feet, the base width (l) is 20 feet, and the height (h) is 25 feet.
Plugging in the values, we get: V = (1/3) * 50 ft * 20 ft * 25 ft
Calculating this expression, we get: V = 83,333.33 ft^3
Therefore, the correct answer is: 8,333.33 ft.3
A rectangular pyramid has a length of 7 cm and a width of 9 cm. Its volume is 231 cubic centimeters. Use the formula for the volume of a pyramid to calculate the height of this pyramid. Show all your work.(2 points)
To find the height of the rectangular pyramid, we can rearrange the formula for volume:
V = (1/3) * l * w * h
Given that the volume is 231 cm^3, the length is 7 cm, and the width is 9 cm, we can plug in these values to the formula:
231 = (1/3) * 7 cm * 9 cm * h
Simplifying the equation:
231 = (63/3) * h
Dividing both sides of the equation by 63/3:
h = 231 รท (63/3)
h = 231 * (3/63)
h = 11 cm
Therefore, the height of the rectangular pyramid is 11 cm.