Question

the radii and the height of the cylinder are in ratio 5 is to 7 and its volume is 550 cm cube find its radius

Answer 1

Given
Ratio of height and radii =5:7

Volume =550cm³

As we know volume of cylinder
$= \pi {r}^{2} h$

Let Radius =5x

Height =7x

550=( 22/7) X (5x)² X 7x


550x7/22 =25x² X 7x

25x7=25x² X 7x

175/25=x² X 7x

X³=175/175

X³=1

$x = \sqrt[3]{1} \\ \\ x = 1$
So radii=5x1=5cm

Height =7x1=7cm

Verification

Volume =22/7 x 5² x 7

Volume =22x25

Volume=550cm³

Verified

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Answer 2

✬ Radius of Cylinder = 5 cm ✬

Step-by-step explanation:

Given:

• Radii and height of Cylinder are in ratio 5:7.
• Volume of cylinder is 550 cm³.

To Find:

• What is Measure of the radius ?

Solution: Let x be the common in given ratio. Therefore

• Radius = 5x
• Height = 7x

★ Volume of cylinder = πr²h cubic units

But volume given is 550 cm³.

A/q

$\implies{\rm }$ πr²h = 550

$\implies{\rm }$ 22/7 x (5x)²(7x) = 550

$\implies{\rm }$ 22/7 x (25x²)(7x) = 550

$\implies{\rm }$ 22/7 x 175x³ = 550

$\implies{\rm }$ 22 x 25x³ = 550

$\implies{\rm }$ 550x³ = 550

$\implies{\rm }$ x³ = 550/550

$\implies{\rm }$ x³ = 1

$\implies{\rm }$ x = ³√1

$\implies{\rm }$ x = 1

Hence, The radius of cylinder = 5(1) = 5 cm and

Height of cylinder = 7(1) = 7 cm.

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★ Verification ★

➯ πr²h cm³ = 550

➯ 22/7 x (5)² x (7) cm³ = 550 cm³

➯ 22/7 x 25 x 7 cm³ = 550 cm³

➯ 22 x 25 cm³ = 550 cm³

➯ 550 cm³ = 550 cm³ { LHS = RHS }

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★ Other Formulae of cylinder ★

→ Total Surface Area = 2πr (h + r) sq units.

→ Curved surface area = 2πrh sq units.