Question : Which of the following statements is not correct?
Option 1: For a given radius and height, a right circular cone has a lesser volume than a right circular cylinder.
Option 2: If the side of a cube is increased by 10%, the volume will increase by 33.1%.
Option 3: If the radius of a sphere is increased by 20%, the surface area will increase by 40%.
Option 4: Cutting a sphere into 2 parts does not change the total volume.
Correct Answer: If the radius of a sphere is increased by 20%, the surface area will increase by 40%.
Solution :
Let the radius of the original sphere = $r$
So, the surface area of the original sphere = $4\pi r^2$
Radius of sphere after 20% increase = $r+\frac{20}{100} =1.2r$
Surface area of new sphere = $4\pi (1.2r^2) = 4\pi r^2 \times 1.44$
Percentage increase in area = $\frac{1.44-1}{1}\times 100 $ = 44%
Hence, the correct answer is "If the radius of a sphere is increased by 20%, the surface area will increase by 40%".
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