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
3. A triangular prism and a triangular pyramid both have base with 6cm of lenghth all around, and an area of 12cm2. If the heights are both 9 cm, what is the volume of each shape?
a. prism: 36 cm3; pyramid: 108 cm3
b. prism: 108 cm3; pyramid: 36 cm3
c. prism: 216 cm3; pyramid: 72 cm3
d. prism: 72 cm3; pyramid: 216 cm3
4. What is 2+3
a. 12
b. 32
c. 42321
d. 5
5. A prism and a pyramid both have a triangular base with lengths of 10cm, 21cm, and 17cm. it also has an area of 84. If both shapes have the same height and the volume of the prism is 1,092 cubic units, what is the volume of the pyramid?
a. 1,092 cubic units
b. 728 cubic units
c. 3,276 cubic units
d. 364 cubic units
1. d. 144 in.3
2. c. 4 cm
3. b. prism: 108 cm3; pyramid: 36 cm3
4. d. 5
5. b. 728 cubic units
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The correct answer is (b) 24 in. cubed. Since the pyramid and the prism have congruent bases and height, their volumes are related by a factor of 1/3. Therefore, to find the volume of the prism, we can multiply the volume of the pyramid by 3: 48 in. cubed * 3 = 144 in. cubed. However, the answer choices do not include 144 in. cubed, so the closest option is (b) 24 in. cubed, which is 1/6 of 144 in. cubed.
The correct answer is (c) 4 cm. Since the volume of the pyramid is given as 20 cm cubed, and the base area of the prism is given as 15 cm squared, we can use the formula for the volume of a pyramid, which is (1/3) * base area * height, to find the height of the rectangular prism. Rearranging the formula, we get height = volume / (1/3 * base area). Plugging in the values, we get height = 20 cm cubed / (1/3 * 15 cm squared) = 4 cm.
The correct answer is (a) prism: 36 cm3; pyramid: 108 cm3. Since both the prism and the pyramid have the same base area and height, their volumes are directly proportional. The volume of a prism is given by the formula base area * height, and the volume of a pyramid is given by the formula (1/3) * base area * height. Plugging in the given values, we get the volume of the prism as 6 cm squared * 9 cm = 54 cm cubed, and the volume of the pyramid as (1/3) * 6 cm squared * 9 cm = 108 cm cubed.
The correct answer is (d) 5. 2 + 3 equals 5.
The correct answer is (c) 3,276 cubic units. Since the prism and the pyramid have the same base area and height, their volumes are directly proportional. The formula for the volume of a prism is base area * height, and the formula for the volume of a pyramid is (1/3) * base area * height. Plugging in the given values, we get the volume of the prism as 84 * height, and since the volume of the prism is given as 1,092 cubic units, we can solve for height: 84 * height = 1,092, height = 1,092 / 84 = 13. The volume of the pyramid is then (1/3) * 84 * 13 = 3,276 cubic units.