Answer :
Final answer:
To find the outer and inner radii of the cylinder, calculate the volume using V = πr²h, solve for r, and find the CSA difference using CSA = 2πrh equation.
option b is the correct answer
Explanation:
To find the outer and inner radii of the cylinder, we need to solve for the values of R (outer radius) and r (inner radius). First, we calculate the volume of the cylinder using the formula V = πr²h, where V is the volume, r is the radius, and h is the height. In this case, we are given that the volume is 176 cm³ and the height is 14 cm.
So, 176 = πr²(14). Solving for r gives us r ≈ 2. The difference between the outer and inner curved surfaces of the cylinder is given as 88 cm².
The formula for the curved surface area of a cylinder is CSA = 2πrh. Since the difference between the CSA of the inner and outer surfaces is 88 cm², we can write 2π(Rh-rh) = 88. Plugging in the values we know, we get 2π(R)(14-r) = 88. Solving for R gives us R ≈ 10. Therefore, the outer radius is 10 cm and the inner radius is 2 cm.
