If each edge of a cube is increased by 50%, the percentage increase in its surface area is
A. 50%
B. 75%
C. 100%
D. 125%
Answers
Given : Each edge of a cube is increased by = 50%
Let original edge of cube = a
Original surface area of cube = 6 a²
After increment ,New edge = a + 50% of a
= a + (50/100) × a
= a + a/2
= (2a + a)/2
New edge = 3a/2
New surface area of cube = 6a²
= 6 × (3a/2)²
= 6 × 9a²/4
= 3 × 9a²/2
= 27a²/2
Increase in area = New surface area of cube - Original surface area of cube
= 27a²/2 - 6a²
= (27a² - 12a²)/2
= 15a²/2
% increase in area = (increased area/original area) × 100
= [(15a²/2)/6a²] × 100
= 15a²/2 × 1/6a² × 100
= 5/4 × 100
= 5× 25
= 125%
Hence, the percentage increase in its surface area is 125%.
Option (D) 125% is correct.
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Answer:
Step-by-step explanation:
After increment ,New edge = a + 50% of a
= a + (50/100) × a
= a + a/2
= (2a + a)/2
New edge = 3a/2
New surface area of cube = 6a²
= 6 × (3a/2)²
= 6 × 9a²/4
= 3 × 9a²/2
= 27a²/2
Increase in area = New surface area of cube - Original surface area of cube
= 27a²/2 - 6a²
= (27a² - 12a²)/2
= 15a²/2
% increase in area = (increased area/original area) × 100
= [(15a²/2)/6a²] × 100
= 15a²/2 × 1/6a² × 100
= 5/4 × 100
= 5× 25
= 125%