A cube of side 4 cm is enlarged by a ratio of 3:1a;what is the volume of:i;the original cube?ii;the enlarged cube?b;By what ratio has the volume been increased. (EXPLAIN)
A cube of side 4 cm is enlarged by a ratio of 3:1
a;what is the volume of:
i;the original cube?
ii;the enlarged cube?
b;By what ratio has the volume been increased.
(EXPLAIN)
a)
i) The original cube has a side length of 4 cm. The volume of a cube is calculated by cubing the length of one side. So, the volume of the original cube is 4 cm x 4 cm x 4 cm = 64 cm³.
ii) The enlarged cube has a ratio of 3:1 compared to the original cube. This means that each side length of the enlarged cube is three times the length of the original cube. Therefore, the side length of the enlarged cube is 4 cm x 3 = 12 cm. The volume of the enlarged cube is calculated by cubing the length of one side: 12 cm x 12 cm x 12 cm = 1,728 cm³.
b) To find the ratio by which the volume has been increased, we can compare the volumes of the enlarged and original cubes. The ratio of the enlarged cube's volume to the original cube's volume is 1,728 cm³ : 64 cm³, which simplifies to 27 : 1.
This means that the volume of the enlarged cube is 27 times greater than the volume of the original cube. Therefore, the volume has been increased by a ratio of 27:1.
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