the cube of side 4 cm is enlarged by a ratio of 3:1
what is the volume of
I. the original cube
ii. the enlarged cube
b] by what radio the volume has been increased ?
To find the volume of a cube, you need to know the length of one side. Let's calculate the volume of both the original and enlarged cube.
I. The original cube:
Given that the side length is 4 cm, the volume of the original cube can be calculated using the formula: V = s^3, where s is the length of a side.
V_original = 4^3
V_original = 64 cm^3
Therefore, the volume of the original cube is 64 cm^3.
II. The enlarged cube:
The ratio of enlargement is 3:1. This means that the sides of the enlarged cube are 3 times longer than the original cube.
Enlarged side length = 3 * original side length
Enlarged side length = 3 * 4 cm
Enlarged side length = 12 cm
To find the volume of the enlarged cube, we'll use the same formula:
V_enlarged = (12 cm)^3
V_enlarged = 1728 cm^3
Therefore, the volume of the enlarged cube is 1728 cm^3.
b] The volume has increased by the ratio of the original volume to the enlarged volume.
Increase ratio = V_enlarged / V_original
Increase ratio = 1728 cm^3 / 64 cm^3
Increase ratio = 27
So, the volume has been increased by a ratio of 27:1.
To find the volume of the original and enlarged cubes, we can use the formula for the volume of a cube, which is given by the equation V = s³, where V represents the volume and s represents the length of one side of the cube.
I. The original cube:
The original cube has a side length of 4 cm. Substituting this value into the formula, we get V = 4³ = 64 cm³. Therefore, the volume of the original cube is 64 cm³.
II. The enlarged cube:
The given ratio of enlargement is 3:1. This means that each side of the original cube is multiplied by 3 to get the length of the corresponding side of the enlarged cube. Thus, the length of each side in the enlarged cube is 4 cm × 3 = 12 cm.
Substituting this value into the formula, we get V = 12³ = 1,728 cm³. Therefore, the volume of the enlarged cube is 1,728 cm³.
b] To find the ratio by which the volume has been increased, we can divide the volume of the enlarged cube by the volume of the original cube.
Ratio of enlargement = Volume of enlarged cube / Volume of original cube
Ratio = 1,728 cm³ / 64 cm³
Ratio = 27
Therefore, the volume has been increased by a ratio of 27:1.
I. V = 4^3
II. (3*4)^3 = 3^3 * V