Question

The lateral surface of a cylinder is developed into a square whose diagonal is √5 cm. The area of the base of the cylinder is

Answer 1

hope this helps u.......

pls mark as brainlist.......

jessy........

Answer 2

Given: The lateral surface of a cylinder is developed into a square whose diagonal is √5 cm.

To find: Area of the base of the cylinder

Solution: The formula for lateral surface area of the cylinder = 2πrh where r is the radius of the cylinder and h is the height of the cylinder.

Now, when the cylinder is developed into the square, the height of cylinder equals the length of each side of the square.

Therefore, each side of the square= h

Length of diagonal of square= h✓2

But, length of diagonal is given as ✓5.

Therefore,

h✓2 = ✓5

=> h = ✓5/✓2

=> h = ✓2.5

Also, since the same cylinder is developed into square, the area is also equal.

Area of square= h×h

Therefore,

2πrh = h × h

=> r = h/2π

Area of base

$= \pi \times {r}^{2}$

$= \pi \times ({ \frac{h}{2\pi} )}^{2}$

$= \frac{ {h}^{2} }{4\pi}$

$= \frac{({ \sqrt{2.5} })^{2} }{4\pi}$

$= \frac{2.5}{4\pi}$

$= \frac{0.625}{\pi}$

Therefore, the area of the base of the cylinder is 0.625/π .