The volume of a regular triangular prism is 6. What will the volume of the prism be if the sides
| July 2, 2021 | education
The volume of a regular triangular prism is 6. What will the volume of the prism be if the sides of its base are tripled and the height reduced by half?
The volume of the prism is equal to the product of the area of the base and the height.
V1 = S main * h = 6.
The area of a regular triangle lying at the base of the prism is equal to: Sbasn = a ^ 2 * √3 / 4. If the edge is increased by 3 times, then the area will increase by 9 times.
Then, if the side is increased by 3 times, and the height is reduced by half, the volume will increase by 9/2 = 4.5 times.
V2 = V1 * 4.5 = 6 * 4.5 = 27 cm2.
Answer: The volume of the prism will be 27 cm2.
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