Niko has an outdoor play tent in the form of a regular triangular pyramid, covered in fabric on all four sides. The surface area of the tent is 100 ft.?, the base is 6 ft., and the slant height is 8 ft. What is the height of the base to the nearest tenth? (1 point)
372 ft
6.5 ft
9.3 ft
57.3
9.3 ft
a right rectangular prism has an area of 20 square units and a height of 3 units. what is the volume?
The volume of a rectangular prism is found by multiplying the area of the base by the height. Given that the area is 20 square units and the height is 3 units:
Volume = area x height = 20 units² x 3 units = 60 cubic units.
and then what is the width?
To find the width we need to know the length of the prism, since the area of the base (which is a rectangle or a square) of a rectangular prism is found by multiplying the length times the width (Area = length * width). If we knew the length, then we would be able to find the width by re-arranging the formula to Width = Area/length. But given the information, we cannot find the width.
A gift box is being constructed in the shape of a right rectangular prism. The base is 15 inches squared and the height is 5 inches. What will the volume of the gift box be? (1 point)
The volume of a rectangular prism is computed by multiplying the area of the base by the height. Given that the area of the base is 15 square inches and the height is 5 inches:
Volume = area x height = 15 square inches x 5 inches = 75 cubic inches.
are you sure
Yes, the volume of a rectangular prism is given by the formula Volume = Area of Base x Height. If the area of the base is 15 square inches and the height is 5 inches, the volume is indeed 15 x 5 = 75 cubic inches.
what is the volume of a rectanglar pyramid with a length of 32 cm, a width of 25 cm, an alltotude of 41 cm?
The volume V of a rectangular pyramid is given by the formula:
V = (L*W*H)/3
where L is the length, W is the width, and H is the height (or altitude).
Plugging in the given values:
V = (32 cm * 25 cm * 41 cm) / 3 = 330,667 cm^3 / 3 = 110,222.33 cm^3
The volume of the rectangular pyramid is approximately 110,222.33 cubic cm.
wrong.
I apologize for the misunderstanding. The volume V of a rectangular pyramid is indeed given by the formula:
V = (L*W*H)/3
where L is the length, W is the width, and H is the height (or altitude).
So plugging the given values would be:
V = (32 cm * 25 cm * 41 cm) / 3 = 10,666.67 cm^3
I apologize for the previous incorrect calculation. The correct volume of the rectangular pyramid is 10,666.67 cubic cm.
32,800
32.67
10,933.33
98.400
The correct volume of the rectangular pyramid is 10,933.33 cubic cm.
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)
The resort is building a rectangular pyramid. The volume of a rectangular pyramid is given by the formula Volume = (length * width * height) / 3.
In this case, the length is 50 feet, the width is 20 feet, and the height (or depth in this case) is 25 feet.
Plugging these values into the formula gives:
Volume = (50 ft * 20 ft * 25 ft) / 3 = 250,000 ft^3 / 3 = 83,333.33 ft^3
The lagoon will hold approximately 83,333.33 cubic feet of water.
wrong
I apologize for the mistake. The correct volume of a rectangular pyramid is indeed given by the formula Volume = (length * width * height) / 3.
For the given dimensions:
length = 50 ft
width = 20 ft
height = 25 ft
We get:
Volume = (50 * 20 * 25) / 3
= 250,000 / 3 = 83,333.33 cubic feet.
Please disregard the previous incorrect calculation. The lagoon holds approximately 83,333.33 cubic feet of water.
25000
8,333.333
95
75000
I apologize for the oversight. The volume of a rectangular pyramid is given by the formula:
Volume = (Length * Width * Height) / 3
Given the Length = 50 feet, Width = 20 feet, and Height = 25 feet, the calculation should be:
Volume = (50 ft * 20 ft * 25 ft) / 3 = 25,000 cubic feet.
So, the lagoon will hold 25,000 cubic feet of water.
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)
The formula for the volume of a pyramid is V = (L*W*H) / 3.
Where:
V = volume,
L = length,
W = width, and
H = height.
The problem gives us the following values:
V = 231 cubic cm,
L = 7 cm, and
W = 9 cm.
We have to solve for H (height).
Substitute the given values into the formula, we get:
231 = (7*9*H) / 3.
Solving this equation for H gives:
231 * 3 = 7 * 9 * H,
693 = 63H.
To find the height, we then divide both sides of the equation by 63:
H = 693 / 63,
So, H = 11 cm.
Therefore, the height of the pyramid is 11 cm.