Each edge of a Cube is increased by 50%. Find the
percentage increase in the surface area.
Answers
Answer :
- 125% is the increase in the surface area
Given :
- Each edge of a cube is increased by 50%
To find :
- The percentage increase in the surface area
Solution :
According to question :
First we need to find the side
- Let the side of the cube be x
Given,
- Each edge of a cube is increased by 50% so,
- x(100 + 50) / 100
⇢ x(100 + 50) / 100
⇢ 1.5x
Side of the cube is 1.5x
We know that
- Surface area of cube is 6(side)²
⇢ Surface area of cube is 6(s)²
⇢ 6(1.5x)²
⇢ 6 × 2.25 x²
Finding the percentage increase in the surface area :
⇢ ((6 × 2.25 x² - 6 x²) / 6 x²) × 100
⇢ 125 %
125% is the increase in the surface area.
Answer:
Given:
If each edge of a cube is increased by 50%
Formula used:
The surface area of cube = 6 side2
Calculation:
According to the question,
Let the side of the cube be x
Each side of the cube increased by 50%.
⇒ x(100 + 50)/100 = 1.5x
The surface area of the cube
⇒ 6 x2
The new surface area of the cube (side = 1.5x)
⇒ 6 × 2.25x2
Increase percentage in the surface area
⇒ ((6 × 2.25 x2 - 6 x2)/6 x2 }× 100
⇒ 125%
∴ The percentage increase in the surface area is 125%.
We know that
50% = 1/2
Let the edge of cube be 2 units
Increased edge = 3 units
Original surface area = 6 × 2 × 2 = 24 units2
Increased surface area = 6 × 3 × 3 = 54 units2
Percentage increase in area = (54 - 24)/24 × 100
∴ Percentage increase in area = 125%
Step-by-step explanation:
Each side of the cube increased by 50%. ∴ The percentage increase in the surface area is 125%.
Thank you