Question

how can i prove that two cylinders are the same with one cylinder radius being 12 and the other with only a diameter of 24 with the same height which is 42

Answer 1

divide the diameter by two

Answer 2

Volume of 1st cylinder =
$\pi {r}^{2} h$
$= \frac{22}{7} \times 144 \times 42$
$= 19008 {cm}^{3}$
Volume of second cylinder=
$\pi {r}^{2} h$
$= \frac{22}{7} \times {( \frac{24}{2} )}^{2} \times 42$
$= 19008 {cm}^{3}$
Thus

Volume of 1st cylinder = Volume of second cylinder


their

radii are equal and heights too



Thus

Curved Surface area of both are equal (use formula to show)


Thus

Both Cylinders are equal in terms of volume and surface area

Both cylinders are same