Use the formula for the lateral area of a cylinder to find a relation between the two radii. Also, use the fact that both cylinders have the same height and the same lateral area.
True
Practice makes perfect
Let's begin by remembering the formula to find the lateral area of a cylinder.
L = 2π r h
Now, let's considers two cylinders C_1 and C_2 such that they have the same height and lateral area.
L_1=L_2 & (I) h_1=h_2 & (II)
⇒
2π r_1h_1 = 2π r_2h_2 h_1=h_2
Let's substitute Equation (II) into Equation (I) and simplify it.
As we can see, we get that the radius of both cylinders is the same. Consequently, the two cylinders have the same dimensions which implies that they have the same volume. So, the given statement is true.
