Question

The volume of Prism Y with dimensions 5 cm, 8 cm, and h cm is _____ cubic centimeters. The possible length, width, and height of Prism Y could be:

a) 240; 5, 8, h
b) 320; 4, 10, h
c) 320; 5, 8, h
d) 240; 4, 10, h

Answer 1

The volume of Prism Y with dimensions 5 cm, 8 cm, and h cm is 40h cm³. The possible length, width, and height of Prism Y could be 5 cm, 8 cm, and 8 cm.

Step-by-step explanation:

The volume of Prism Y can be calculated using the formula V = lwh, where l, w, and h represent the length, width, and height of the prism, respectively. In this case, the dimensions given are 5 cm, 8 cm, and h cm. Therefore, the volume of Prism Y is 5 cm × 8 cm × h cm = 40h cm³.

To find the possible dimensions, we need to substitute the given options into the formula and solve for h. Let's go through each option:

1. Option a) 240; 5, 8, h: Volume = 5 cm × 8 cm × h cm = 40h cm³, which is not equal to 240 cm³.
2. Option b) 320; 4, 10, h: Volume = 4 cm × 10 cm × h cm = 40h cm³, which is not equal to 320 cm³.
3. Option c) 320; 5, 8, h: Volume = 5 cm × 8 cm × h cm = 40h cm³, which is equal to 320 cm³. Therefore, the possible dimensions for Prism Y are 5 cm, 8 cm, and 8 cm.
4. Option d) 240; 4, 10, h: Volume = 4 cm × 10 cm × h cm = 40h cm³, which is not equal to 240 cm³.

Hence, the correct option is c) 320; 5, 8, h.