Question

Calculate the plane surface of cylinder having the curved surface area 1848sq.cm and sum of radius and height 35cm

Answer 1

To calculate the plane surface area of a cylinder, subtract the area of the two circular bases from the curved surface area. Use the given formula and equations to find the radius and height, then calculate the area of one circular base. Finally, subtract the area of the bases from the curved surface area to find the plane surface area.

Step-by-step explanation:

To calculate the plane surface area of a cylinder, we need to subtract the area of the two circular bases from the curved surface area.

The formula for finding the curved surface area of a cylinder is given as:

CSA = 2πrh

So, the curved surface area is 1848 cm² and the sum of the radius and height is 35 cm. We can use these values to find the radius and height of the cylinder.

Solving the equation 2πrh = 1848 and r + h = 35 simultaneously will give us the values of r and h.

Once we have the values of r and h, we can calculate the area of one circular base using the formula Area = πr². Finally, we can calculate the plane surface area by subtracting the area of the two circular bases from the curved surface area.

Answer 2

Area of plane surface of cylinder = 2772 sq.cm.

Step-by-step explanation:

Let r be the radius and h be the height of the cylinder.

Curved Surface Area = 1848 sq.cm

2πrh = 1848

2×
`(22)/(7)`×rh = 1848

rh = 1848 ×
`(7)/(22)` ×
`(1)/(2)`

rh = 294

Sum of radius and height = 35

r + h = 35 --- (1)

Now,

r - h =
`\sqrt{(r+h)^(2)-4rh }`

=
`\sqrt{35^(2)-4(294) }`

=
`√(1225-1176)`

=
`√(49)`

= 7

r - h = 7 --- (2)

Adding (1) and (2),

2r = 42

r = 21 cm.

Area of the plane surface = 2 × π
`r^(2)`

= 2 ×
`(22)/(7)` × 21 × 21

= 2772 sq.cm.