the length of each edge of a cube is of length 3m. the edges are increased by 20%. Calculate the percentage increase in the volume of the cube.
that would be 1.20^3 = 1.728 or 72.8% increase
To calculate the percentage increase in the volume of the cube when the edges are increased by 20%, follow these steps:
Step 1: Find the original volume of the cube.
Since all the edges of the cube have a length of 3m, the original length of each edge (L) is 3m. Therefore, the original volume (V) of the cube can be calculated using the formula: V = L^3.
V = 3m × 3m × 3m
V = 27m^3
So, the original volume of the cube is 27 cubic meters.
Step 2: Calculate the new length of each edge.
When the edges are increased by 20%, the new length of each edge is 3m + 0.2 × 3m = 3m + 0.6m = 3.6m.
Step 3: Find the new volume of the cube.
Using the new length of each edge (3.6m), calculate the new volume (V_new) of the cube using the formula: V_new = L_new^3.
V_new = 3.6m × 3.6m × 3.6m
V_new = 46.656m^3
So, the new volume of the cube is approximately 46.656 cubic meters.
Step 4: Calculate the percentage increase in the volume.
To find the percentage increase in the volume, use the formula: Percentage Increase = ((V_new - V) / V) × 100.
Percentage Increase = ((46.656m^3 - 27m^3) / 27m^3) × 100
Percentage Increase ≈ 72.8%
Therefore, the percentage increase in the volume of the cube when the edges are increased by 20% is approximately 72.8%.
To calculate the percentage increase in volume, we need to find the new volume of the cube after the edges are increased by 20%.
First, let's find the original volume of the cube:
Original length of each edge = 3m
Original volume of the cube = (Original length of each edge)^3 = 3^3 = 27 cubic meters
Next, let's calculate the new length of each edge after a 20% increase:
Increase in length = 20% of original length = 20/100 * 3m = 0.6m
New length of each edge = Original length + Increase in length = 3m + 0.6m = 3.6m
Finally, let's calculate the new volume of the cube:
New volume of the cube = (New length of each edge)^3 = 3.6^3 = 46.656 cubic meters
Now, we can calculate the percentage increase in the volume:
Percentage increase in volume = ((New volume - Original volume) / Original volume) * 100%
= ((46.656 - 27) / 27) * 100%
= (19.656 / 27) * 100%
≈ 72.8%
Therefore, the percentage increase in the volume of the cube when the edges are increased by 20% is approximately 72.8%.