Question

A rectangle of length 66 cm and breadth 14 cm is rolled into a cylinder. Find total surface area of the cylinder

Answer 1

circumference of base of cylinder=66cm

2×π×r=66cm

r=66×7/22×2

r=10.5cm

h=14cm

T.S.A of cylinder=2πr(r+h)

2×22/7×10.5(10.5+14)

44×1.5(24.5)

66×24.5

1617cm square

Answer 2

$\underline\mathfrak\pink{Answer:—}$

$\fbox\purple{total~ surface~ area ~of~ the ~cylinder~ = ~1617~cm²}$

________________________

$\underline\mathfrak\pink{Explanation:—}$

[Hint : When the paper is rolled into a cylinder along the length, the length of the paper becomes the circumference of the base of the cylinder and the breadth of the paper becomes the the cylinder.]

.

Height of cylinder = 14 cm

Circumference of base = 2πr = 66 cm

Radius of cylinder

$\\ \\ = \: \dfrac{66 \times 7}{2 \times 22} \: = \: 10.5 \: cm$

.

Total surface area of the cylinder = 2πr(r + h)

$\\ \\ = \: 2 \times \dfrac{22}{7} \times 10.5 \times 24.5 \\ \\ = \: 1617 \: cm {}^{2}$