If each edge of a cube is increased by 25
Asked by admin @ in Math viewed by 325 People
. If each edge of a cube is increased by 25%, then find the percentage increase in its surface area.
Answered by admin @
GIVEN :-
- Each edge of cube is increased by 25%.
TO FIND :-
- % increase in its surface area.
TO KNOW :-
★ Area of cube = 6 × edge
SOLUTION :-
Let us consider , the initial edge of cube be 'x'.
We know , surface area of cube = 6×edge
Initial area = 6x
Now each edge of cube is increased by 25%.
→ New edge = x + 25% of x
→ New edge = x + (25/100) x
→ New edge = x + x/4
→ New edge = 5x/4
♦ New area = 6 × (5x/4)
♦ New area = 30x/4
♦ New area = 15x/2
______________________
% Increase in area
= [ (New area - initial area) / initial area ] × 100
= [ ( 15x/2 - 6x ) / 6x ] × 100
= [ ( 3x / 2 ) / 6x ] × 100
= [ 3x / 12x ] × 100
= [ 1/4 ] × 100
= 25
Hence , there is 25% increase in area when edge of cube is increased by 25%.
MORE TO KNOW :-
★ Area of Cylinder = πr²h
★ Area of Cone = (1/3) πr²h
★ Area of Cuboid = l × b × h
★ Area of Sphere = (4/3) πr³
★ Area of hemisphere = (2/3) πr³
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