Question

A rectangular piece of paper 11cm × 4cm is folded without overlapping to make a

cylinder of height 4cm. Find :-

(i) The volume of the cylinder.

(ii) The lateral surface area of the cylinder

(iii) The total surface area of the cylinder if it is closed at one end and open at the

other.

(iv) Quantity of water that can be stored in a plastic cylinder of same measure.​

Answer 1

Explanation:

Given,

Rectangular paper of length (l) = 11 cm

Breadth (b) = 4 cm

When rectangular paper is folded to form a cylinder

length will be equal to circumference of top of cylinder and height is equal to breadth

so, b = h = 4cm

l=

$l \: = 2\pi \: r$

Putting in the values we will r

11 = 2× 22/7 ×r

(11×7)/2×22 = r

flipping the equation

r = (11×7)/2×22

=7/14

=1/2

=0.5 cm

i) Volume of cylinder =

$\pi \: {r}^{2} h$

= 3.14×(0.5)^2×4

= 3.14 cu. cm

ii) Lateral surface area of cylinder =

$2\pi \: r \: h$

Putting in the values

= 2×3.14×0.5×4

= 12.56 sq.cm

iii) Total surface area of cylinder with one end closed =

$2\pi \: rh + \pi {r}^{2}$

Putting in the values

= 2×3.14×0.5×4 + 3.14×0.5×0.5

=12.56+ 0.785

= 13.345 sq.cm

iv) Quantity of water that can be stored= Volume of cylinder

I.e 3.14 l