Question

Under some transformation, a cuboid C whose base area is 30 , cm² is mapped onto a similar cuboid C₂ with a base area of 120 , cm². If the volume of the cuboid C is 450 , cm³, find the volume of the cuboid C₂ in liters.

a) 1.2 L
b) 2.4 L
c) 3.6 L
d) 4.8 L

Answer 1

Using the ratio of the base areas to determine the scale factor, we find that the volume of cuboid C₂ is 8 times that of cuboid C, yielding a volume of 3600 cm³ or 3.6 L. Hence, the correct answer is 3.6 L.

Step-by-step explanation:

The student is asking about the transformation of a cuboid and the resulting volume of the transformed cuboid. Given that the base area of the original cuboid (C) is 30 cm² and its volume is 450 cm³, and knowing that its similar cuboid (C₂) has a base area of 120 cm², we can find the volume of the similar cuboid C₂ by finding the scale factor and applying it to the volume of C.

The base areas are in the ratio of 30 cm² to 120 cm², which simplifies to a ratio of 1:4. Since both cuboids are similar, the length, width, and height of C₂ would all be twice that of C (since the square root of 4 is 2). Therefore, the volume of C₂ would be 2³ (or 8) times the volume of C.

So, the volume of C₂ is 450 cm³ * 8 = 3600 cm³. To convert this volume to liters, we use the conversion factor that 1 liter equals 1000 cm³. Therefore, the volume of C₂ is 3600 cm³ / 1000 cm³/L = 3.6 L.

The correct answer to the student's question is 3.6 L, which is answer option c).