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
a. 16 in. cubed
b. 24 in. cubed
c. 96 in. cubed
d. 144 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?
a. 4/3 cm
b. 20 cm
c. 4 cm
d. 5 cm
11 answers
c. 4 cm
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
a. 16 in. cubed
b. 24 in. cubed
c. 96 in. cubed
d. 144 in.3
a. 16 in. cubed
b. 24 in. cubed
c. 96 in. cubed
d. 144 in.3
d. 144 in.3
how do you find the volume of a triangular prism
To find the volume of a triangular prism, you need to multiply the area of the base (which is a triangle) by the height of the prism. So, the formula for the volume of a triangular prism is:
V = (1/2) * b * h * H
where:
- b: length of the base of the triangle
- h: height of the triangle
- H: height of the prism
You can simplify the formula to:
V = (1/2) * Bh
where B is the area of the base (which is equal to (1/2) * b * h).
V = (1/2) * b * h * H
where:
- b: length of the base of the triangle
- h: height of the triangle
- H: height of the prism
You can simplify the formula to:
V = (1/2) * Bh
where B is the area of the base (which is equal to (1/2) * b * h).
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
144 in.3
16 in.3
96 in.3
24 in.3
Responses
144 in.3
16 in.3
96 in.3
24 in.3
The answer is 144 in.3.
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
, 20 cm
4 cm
4 cm
43 cm
, Start Fraction 4 over 3 End Fraction cm
5 cm
Responses
20 cm
, 20 cm
4 cm
4 cm
43 cm
, Start Fraction 4 over 3 End Fraction cm
5 cm
The answer is 4 cm.
Use the image to answer the question.
An illustration shows an equilateral triangle with each side measuring 6 centimeters. The perpendicular height is shown as a dashed line from the base to the apex and and is 4 centimeters. A right angle symbol is shown to the right of the perpendicular line.
Use the model for the base of a triangular prism and triangular pyramid. If the heights are both 9 cm, what is the volume of each shape?
(1 point)
Responses
prism: 216 cm3; pyramid: 72 cm3
prism: , 216 cm cubed, ; pyramid: , 72 cm cubed
prism: 72 cm3; pyramid: 216 cm3
prism: , 72 cm cubed, ; pyramid: , 216 cm cubed
prism: 36 cm3; pyramid: 108 cm3
prism: , 36 cm cubed, ; pyramid: , 108 cm cubed
prism: 108 cm3; pyramid: 36 cm3
prism: , 108 cm cubed, ; pyramid: , 36 cm cubed
An illustration shows an equilateral triangle with each side measuring 6 centimeters. The perpendicular height is shown as a dashed line from the base to the apex and and is 4 centimeters. A right angle symbol is shown to the right of the perpendicular line.
Use the model for the base of a triangular prism and triangular pyramid. If the heights are both 9 cm, what is the volume of each shape?
(1 point)
Responses
prism: 216 cm3; pyramid: 72 cm3
prism: , 216 cm cubed, ; pyramid: , 72 cm cubed
prism: 72 cm3; pyramid: 216 cm3
prism: , 72 cm cubed, ; pyramid: , 216 cm cubed
prism: 36 cm3; pyramid: 108 cm3
prism: , 36 cm cubed, ; pyramid: , 108 cm cubed
prism: 108 cm3; pyramid: 36 cm3
prism: , 108 cm cubed, ; pyramid: , 36 cm cubed
The volume of the triangular prism is 108 cm3 and the volume of the triangular pyramid is 36 cm3.
To calculate the volume of the prism, we use the formula:
V = base area * height
The base area of the prism is (1/2) * 6 * 4 = 12 cm2 (half the area of the equilateral triangle).
Therefore, V = 12 * 9 = 108 cm3.
To calculate the volume of the pyramid, we use the formula:
V = (1/3) * base area * height
The base area of the pyramid is also 12 cm2.
Therefore, V = (1/3) * 12 * 9 = 36 cm3.
To calculate the volume of the prism, we use the formula:
V = base area * height
The base area of the prism is (1/2) * 6 * 4 = 12 cm2 (half the area of the equilateral triangle).
Therefore, V = 12 * 9 = 108 cm3.
To calculate the volume of the pyramid, we use the formula:
V = (1/3) * base area * height
The base area of the pyramid is also 12 cm2.
Therefore, V = (1/3) * 12 * 9 = 36 cm3.
1 answer