A cylinder has a curved surface area equal to 350% of the curved surface area of another cylinder. If their radii are in the ratio 3 : 1, then the volume of the smaller cylinder is approximately _____% of the larger cylinder (the smaller cylinder has its radius and height smaller when compared to the larger).

Correct option is A

Given:
Ratio of radius of cylinders= 3:1
Curved surface area of one cylinder = 350% of smaller cylinder
Formula Used:
Curved surface area = 2π rh
Volume =π $$r^2$$​h
Solution:
Let the radius of larger cylinder and smaller cylinder be 3x and x
Height of both cylinder be $$h_1 \, and\, h_2$$​​
​$$CSA_1 = 350\% \,of \,CSA_2$$​​
​$$2\pi \cdot 3x \cdot h_1 = 3.5 \cdot 2\pi \cdot 3x \cdot h_2\\\frac{h_1}{h_2} = \frac{3.5}{3} = \frac{7}{6}$$​​
Volume of larger cylinder = π ×$$(3x)^2$$​×7
Volume of smaller cylinder = π ×$$x^2$$​×6
Percentage of volume of smaller cylinder to volume of larger cylinder
​$$\frac{\pi \times x^2 \times 6}{\pi \times (3x)^2 \times 7} \times 100\\= \frac{6}{63} \times 100\\= 9.52\%$$​​