Question

What would be the volume of this solid if the height were halved and the other dimensions were reduced proportionally? Round to the nearest whole number.

The image?is of a?parallelogram prism standing on its face and making an angle of 60 degrees with horizontal. The dimension of prism is 3 cm by 4cm by 10 cm.

Answer 1

The volume of the solid would be 60 cubic centimeters.

Step-by-step explanation:

To find the volume of the solid when the height is halved and the other dimensions are reduced proportionally, we can use the formula for the volume of a parallelogram prism. The formula is V = Bh, where B is the area of the base and h is the height. In this case, the base is a parallelogram with side lengths of 3 cm and 4 cm, and the height is 10 cm.

1. Find the area of the base by multiplying the base length (3 cm) by the base width (4 cm). The area is 3 cm × 4 cm = 12 cm².
2. Halve the height by dividing it by 2. The new height is 10 cm ÷ 2 = 5 cm.
3. Calculate the volume by multiplying the base area (12 cm²) by the new height (5 cm). The volume is 12 cm² × 5 cm = 60 cm³.
4. Round the volume to the nearest whole number. In this case, the volume is already a whole number, so the rounded volume is still 60 cm³.