Greg made two similar glass display boxes shaped like triangular prisms. The length of the sides of the base of the first display box is 5 feet, and the length of the sides of the base of the second display box is 10 feet. If the volume of the first display box is 52 ft3, what is the volume of the second display box?
Answer
A. 104 ft3
B. 208 ft3
C. 260 ft3
D. 416 ft3
To find the volume of the second display box, we need to determine the ratio between the volumes of the two boxes.
The volume of a triangular prism can be calculated using the formula: V = (1/2) * base * height * length, where the base is the area of the triangular base and the height is the perpendicular distance from the base to the opposite face.
Since the two display boxes are similar, their corresponding sides will have a constant ratio. The ratio of the lengths of the bases of the two boxes is 10/5 = 2.
It is known that the volume of the first display box is 52 ft^3. Therefore, to find the volume of the second display box, we can use the following equation:
V_2 = V_1 * (ratio)^3
V_2 = 52 * (2)^3
= 52 * 8
= 416 ft^3
Therefore, the volume of the second display box is 416 ft^3, which corresponds to option D.