1. There is a rectangular prism and pyramid with congruent bases and height. If the volume of the pyramid is 48 in.3, what is the volume of the prism?(1 point) Responses 16 in.3 , 16 in. cubed 144 in.3 144 in. cubed 96 in.3 , 96 in. cubed 24 in.3
2. A rectangular prism has a base area of 15 cm2, and a congruent pyramid has a volume of 20 cm3. What is the height of the rectangular prism?(1 point)
Responses 20 cm 4 cm 5 cm 4/3 cm
1. 144 in. cubed
2. 4 cm
1. To find the volume of the rectangular prism, we need to know the formula for the volume of a pyramid. The formula is: Volume = (1/3) * Base Area * Height. Since the pyramid and prism have congruent bases and height, the base area and height of the pyramid is the same as that of the prism.
Given that the volume of the pyramid is 48 in.3, we can substitute this value into the formula and solve for the base area multiplied by the height (Base Area * Height).
48 in.3 = (1/3) * Base Area * Height
Multiplying both sides of the equation by 3 gives us:
144 in.3 = Base Area * Height.
Therefore, the volume of the rectangular prism is 144 in.3.
2. The volume of a rectangular prism is given by the formula: Volume = Base Area * Height. we are given that the base area of the prism is 15 cm2, and the volume of the pyramid is 20 cm3.
Therefore, we can set up the equation:
20 cm3 = 15 cm2 * Height
Dividing both sides of the equation by 15 cm2 gives us:
Height = 20 cm3 / 15 cm2 = 4/3 cm.
Therefore, the height of the rectangular prism is 4/3 cm.
1. To find the volume of the prism, we first need to identify the relationship between the volume of the prism and the volume of the pyramid. Since the bases of the prism and pyramid are congruent (meaning they have the same dimensions), the area of their bases is the same.
The formula for the volume of a rectangular prism is given by: Volume = Base Area x Height.
Similarly, the formula for the volume of a pyramid is given by: Volume = (1/3) x Base Area x Height.
Given that the volume of the pyramid is 48 in.3, we can substitute this value into the pyramid volume formula: 48 = (1/3) x Base Area x Height.
Now, since the bases are congruent, we can write the equation as: 48 = (1/3) x Base Area x Height.
Next, we need to solve for the base area. Unfortunately, the given information does not provide the base area. Therefore, we cannot determine the volume of the prism without this information.
2. To find the height of the rectangular prism, we need to utilize the relationship between the base area and the volume of the pyramid.
Given that the base area of the prism is 15 cm2, we can substitute this value into the base area of the pyramid.
The formula for the volume of a pyramid is given by: Volume = (1/3) x Base Area x Height.
Given that the volume of the pyramid is 20 cm3 and the base area is 15 cm2, we can substitute these values into the volume formula: 20 = (1/3) x 15 x Height.
To solve for the height, we multiply both sides of the equation by 3 to get rid of the fraction: 60 = 15 x Height.
Finally, we can solve for the height by dividing both sides of the equation by 15: Height = 60/15 = 4 cm.
Therefore, the height of the rectangular prism is 4 cm.