Question

the area of base of a cylinder IS 308 m^2 and its volume is 1540 metre cube find the circumference of the base and curved surface area

Answer 1

ANSWER:

• Circumference of the base = 44√2 m

• Curved surface area of cylinder = 220√2 m²

GIVEN:

• Base area of cylinder = 308 m²

• Volume of cylinder = 1540 m³

TO FIND:

• Circumference of the base

• Curved surface area of cylinder

EXPLANATION:

$\boxed{ \large{ \bold{Area \: of \: circle = \pi {r}^{2} }}}$

π r² = 308 m²

r² = (308 × 7 ) ÷ 22

r² = 14 × 7

r² = 7 × 7 × 2

r = 7 × √2

r = 7√2 m

$\boxed { \large { \bold {Volume\:of\:cylinder=\pi r^2h }}}$

π r² h = 1540

Substitute π r² = 308 m²

308 h = 1540

h = 1540/308

h = 5 m

$\boxed{ \large{ \bold{Circumference \: of \: circle = 2 \pi {r} }}}$

Circumference of base = 2 × 22/7 × 7√2

Circumference of base = 2 × 22 × √2

Circumference of base = 44√2

Circumference of base = 44√2 m

$\boxed{ \large{ \bold{C.S.A \: of \: cylinder = 2 \pi rh }}}$

C.S.A = Curved Surface Area

C.S.A = 2πr × h

Substitute 2πr = 44√2 m

C.S.A = 44√2 × 5

C.S.A = 220√2 m²

Curved Surface Area of cylinder = 220√2 m²

Hence Circumference of the base = 44√2 m and Curved surface area of cylinder = 220√2 m²

Answer 2

$\large\underline{\underline{\pink{\sf Answer}}}$

☞ Circumference = 44√2 m

☞ CSA = 220√2 m²

$\large\underline{\underline{\green{\sf Given}}}$

✭ Area of a cylinder is 308 m²

✭ Volume of the cylinder is 1540 m³

$\large\underline{\underline{\red{\sf To \ Find}}}$

◈ The circumference of the base?

◈ Curved Surface Area?

$\large\underline{\underline{\blue{\sf Steps}}}$

First of all we shall find the radius of the circle,so here the base of a cylinder is a circle so,

$\underline{\boxed{\sf Area \ of \ circle = \pi r^2}}$

Substituting the values,

➝ πr² = 308 m²

➝ r² = 308 × (7/22)

➝ r² = 14 × 7

➝ r = √7×2×7

➝ r = 7√2 m

So now the volume of the cylinder is given by,

$\underline{\boxed{\sf Volume \ of \ cylinder = \pi r^2 h}}$

Substituting the given values,

➢ 308 × h = 1540

➢ h = 1540/308

➢ h = 5 m

So now that we know the radius then the circumference will be,

$\underline{\boxed{\sf Circumference \ of \ circle= 2 \pi r }}$

Substituting the Values known,

➳ 2 × 22/7 × 7√2

➳ 2 × 22 × √2

➳ Circumference = 44√2 m

And finally the CSA of a cylinder is given by,

$\underline{\boxed{\sf CSA \ of \ cylinder = 2 \pi rh}}$

➠ 2 × 22/7 × 7√2 × 5

➠ 44√2 × 5

➠ 220√2 m²

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