A rectangular prism has a base area of 15 cm2 , and pyramid with a congruent base and height has a volume of 20 cm3 . What is the height of the rectangular prism?(1 point)
Responses
4 cm
4 cm
43 cm
Start Fraction 4 over 3 End Fraction cm
20 cm
20 cm
5 cm
5 answers
4 cm
why
The volume of the pyramid is given as 20 cm^3, and the base area is 15 cm^2. We can find the height of the pyramid by dividing the volume by the base area:
Volume = (1/3) * base area * height
20 cm^3 = (1/3) * 15 cm^2 * height
20 cm^3 = 5 cm * height
height = 20 cm^3 / 5 cm
height = 4 cm
Therefore, the height of the rectangular prism is 4 cm.
Volume = (1/3) * base area * height
20 cm^3 = (1/3) * 15 cm^2 * height
20 cm^3 = 5 cm * height
height = 20 cm^3 / 5 cm
height = 4 cm
Therefore, the height of the rectangular prism is 4 cm.
Relationship Between Volume of Prisms & Pyramids Quick Check
3 of 53 of 5 Items
Question
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
3 of 53 of 5 Items
Question
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
To find the volume of a prism, you use the formula: Volume = base area * height.
In this case, the base of the prism is an equilateral triangle with side length 6 cm, so the area of the base can be calculated using the formula for the area of an equilateral triangle: A = (sqrt(3)/4) * s^2, where s is the side length.
Base area of prism = (sqrt(3)/4) * 6^2 = (sqrt(3)/4) * 36 = 9sqrt(3) cm^2.
Volume of prism = base area * height = 9sqrt(3) cm^2 * 9 cm = 81sqrt(3) cm^3.
To find the volume of a pyramid, you use the formula: Volume = (1/3) * base area * height.
Base area of pyramid = 9sqrt(3) cm^2.
Volume of pyramid = (1/3) * 9sqrt(3) cm^2 * 9 cm = 27sqrt(3) cm^3.
Therefore, the correct response is:
prism: 81sqrt(3) cm^3; pyramid: 27sqrt(3) cm^3.
In this case, the base of the prism is an equilateral triangle with side length 6 cm, so the area of the base can be calculated using the formula for the area of an equilateral triangle: A = (sqrt(3)/4) * s^2, where s is the side length.
Base area of prism = (sqrt(3)/4) * 6^2 = (sqrt(3)/4) * 36 = 9sqrt(3) cm^2.
Volume of prism = base area * height = 9sqrt(3) cm^2 * 9 cm = 81sqrt(3) cm^3.
To find the volume of a pyramid, you use the formula: Volume = (1/3) * base area * height.
Base area of pyramid = 9sqrt(3) cm^2.
Volume of pyramid = (1/3) * 9sqrt(3) cm^2 * 9 cm = 27sqrt(3) cm^3.
Therefore, the correct response is:
prism: 81sqrt(3) cm^3; pyramid: 27sqrt(3) cm^3.