Question

Please give the solution of both of them ​

Answer 1

Answer:

21.

Let radius be 7x and height be 3x.

Volume =12474cm³

=πr²h=12474cm³

=22/7×(7x)²×3x=12474

=22×7x²×3x=12474

=x³=12474/(22×21)

=x³=27

=x=3

i.e., radius =7x=7×3=21cm

height =3x=3×3 =9cm

Now, CSA of cylinder

=2πrh

=2×22/7×21×9

=1188cm²

TSA of cylinder

=2πr(h+r)

=2×22/7×21(9+21)

=3960cm²

22.

Given:

radius,r =36cm=0.36m

height, h=3.5m

Now, cost of painting 20 cylindrical pillars at Rs 3 per m²

=Rs 3 ×20 ×CSA of pillar

= Rs 60× 2πrh

= Rs 60 × 2×22/7 × 0.36 ×3.5

= Rs 475.2

Answer 2

Answer:

21 )

Radius of cylinder is 21cm,

Height of cylinder is 9 cm.

Curved surface area of cylinder is 1188 cm^2.

And

Total surface area of cylinder is 3960 cm^2.

22)

Cost of painting at the rate of rs 3 per square meter = rs 475.2

Step-by-step explanation:

Given

Volume of cylinder is 12474 cm^3

Let the radius of cylinder be 7 x

And

Height of cylinder be 3 x respectively.

According to the question

Volume of cylinder = 12474 cm^3

$\pi {r}^{2} h \: = \: 12474 \: {cm}^{3} \\ \frac{22}{7} \: \times \: 7x \: \times \: 7x \: \times \: 3x \: = \: 12474 \: {cm}^{3} \\ {22} \: \times \: x \: \times \: 7x \: \times 3x \: = \: 12474 {cm}^{3} \\ 22 \: \times \: 21 {x}^{3} \: \: \: = \: 12474 \: {cm}^{3} \\ 462 \: {x}^{3} \: \: = \: 12474 \: {cm}^{3} \\ {x}^{3} \: = \: \frac{12474}{462} \: { \: cm}^{3} \\ {x}^{3} \: = \: 27 \: {cm}^{3} \\ x \: = \: \sqrt[3]{27 \: cm ^{3} } \\ x \: = \: \sqrt{3cm \times \: 3cm \times \: 3cm} \\ x = \: 3cm$

7x = 7 × 3 cm = 21 cm

3x = 3 × 3 cm = 9 cm

Hence

Radius of cylinder (r) = 7 x = 21 cm

And

Height of cylinder (h) = 3x = 9 cm.

$curved \: surface \: area \: o f \: cylinder \: = \: 2\pi \: rh \\ curved \: surface \: area \: of \: cylinder \: = \: 2 \times \frac{22}{7} \times 21cm \: \times 9cm \\ curved \: surface \: area \: of \: cylinder \: = 2 \times 22 \: \times \: 3cm \: \times 9 \: cm \\ curved \: surface \: area \: of \: cylinder = \: </u></em><em><u>4</u></em><em><u>4</u></em><em><u>\: \times {27cm}^{2} \\ curved \: surface \: area \: of \: cylinder \: = \: {1</u></em><em><u>1</u></em><em><u>8</u></em><em><u>8</u></em><em><u> \: cm}^{2}$

Curved surface area of cylinder os 1188 cm &^2.

$total \: surface \: area \: of \: cylinder \: = \: 2\pi \:r (r \: + \: h) \\ total \: surface \: area \: of \: cylinder \: = \: 2 \: \times \: \frac{22}{7} \: \times 21 \: (9 \: + \: 21) \: {cm}^{2} \\ total \: surface \: area \: of \: cylinder \: = \: 2 \: \times 22 \: \times 3 \: \times 30 \: {cm}^{2} \\ total \: surface \: area \: of \: cylinder \: = \: 44 \: \times 90 \: {cm}^{2} \\ total \: surface \: area \: of \: cylinder \: = \: 3960 \: {cm}^{2}$

Total surface area of cylinder is 3960 cm^2.

22) Given

Radius of one piller = 36 cm = 0.36 m

Height of one piller = 3.5 m

Curved surface area of one piller = 2πrh

Curved surface area of one piller = 2 ×22/7 × 0.36 × 3.5 cm^2

Curved surface area of one piller = 2 × 22 × 0.36 × 0.5 cm^2

Curved surface area of one piller = 7.92 cm^2

Curved surface area of 20 such pillers = 20 × 7.92 cm^2

Curved surface area of 20 such pillers = 158.4 cm^2

Cost of painting at the rate of rs 3 per square meter = 3 × 158.4

Cost of painting at the rate of rs 3 per square meter = rs 475.2