Which of the following statements is not correct ?

(A) : Volume of cylinder = $$\pi r^2h$$

Volume of cone = $$\frac{1}{3}\pi r^2h$$

=> Volume of cone is lesser (one-third) than the volume of cylinder. Above statement is correct.

(B) : Let side of cube = $$a=10$$ cm

=> Volume of cube = $$(10)^3=1000$$ $$cm^3$$

New side after 10% increase = $$10+(\frac{10}{100}\times10)=11$$ cm

Thus, new volume = $$(11)^3=1331$$ $$cm^3$$

$$\therefore$$ Increase in volume = $$\frac{(1331-1000)}{1000}\times100=33.1\%$$

Thus, above statement is correct.

(C) : Let radius of sphere = $$r=10$$ cm

Surface area of sphere = $$4\pi r^2=4\pi(10)^2=400\pi$$ $$cm^2$$

After increasing the radius by 20%, new radius = $$r'=10+(\frac{20}{100}\times10)=12$$ cm

=> New surface area = $$4\pi(12)^2=576\pi$$ $$cm^2$$

$$\therefore$$ Increase in surface area = $$\frac{(576-400)}{400}\times100=44\%$$

Thus, above statement is not correct.

(D) : Cutting a sphere into 2 parts does not change the total volume because the sum of volume of the two hemispheres will be equal to the volume of sphere. Hence, it is also correct.

=> Ans - (C)