Question

The radius and height of a cylinder are in the ratio 4:7. Find the diameter of the
cylinder if its volume is 1188cm³.​

Answer 1

Given :

• Radius of cylinder : Height of cylinder = 4:7
• Volume of cylinder = 1188 cm³

To find :

Diameter of cylinder

Formula used:

• Volume of cylinder = πr²h
• Diameter = 2r

Solution :

Radius of cylinder : Height of cylinder = 4:7

$\sf \implies \dfrac{Radius}{ \: Height} \: = \: \dfrac{4}{7}$

$\sf \implies \: Height \: = \: \dfrac{7}{4} \times Radius$

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Now ,

Let radius = r

➝ Height = 7r/4

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Volume of cylinder = π r² h

$\sf \implies \:Volume \: of \: cylinder \: = \: \pi r^2 \bigg( \dfrac{7r}{4} \bigg)$

$\sf \implies \:1188 \: {cm}^{3} \: = \: \dfrac{22}{7} r^2 \bigg( \dfrac{7r}{4} \bigg)$

$\sf \implies \:1188 \: {cm}^{3} \: = \: \dfrac{11}{2} r^3$

$\sf \implies \: r^3 = 1188 \: {cm}^{3} \times \dfrac{2}{11}$

$\sf \implies \: r^3 = 108 \times 2 \: {cm}^{3}$

$\sf \implies \: r^3 = 216 \: {cm}^{3}$

$\sf \implies \: r^3 = \: {(6 \: cm )}^{3}$

$\sf \implies \: r = 6cm$

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➝ Diameter = 2r

➝ Diameter = 2(6 cm)

➝ Diameter = 12cm

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ANSWER : 12 cm

Answer 2

Answer:

$Volumeofcylinder=πr2(47r)\sf \implies \:1188 \: {cm}^{3} \: = \: \dfrac{22}{7} r^2 \bigg( \dfrac{7r}{4} \bigg) \\ 1188cm3=722r2(47r)\sf \implies \:1188 \: {cm}^{3} \: = \: \dfrac{11}{2} r^3 \\⟹1188cm3=211r3 \\ \sf \implies \: r^3 = 1188\: {cm}^{3} \times \dfrac{2}{11} \⟹r3=1188cm3×112\sf \implies \: r^3 = 108\times 2 \: {cm}^{3} \\ \\ ⟹r3=108×2cm3</p><p>\sf \implies \: r^3 = 216 \: {cm}^{3} \\⟹r3=216cm3\sf \implies \: r^3 = \: {(6 \: cm )}^{3} \\ ⟹r3=(6cm)3\sf \implies \: r = 6cm \\ \\ ⟹r=6cm$