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

2 thoughts on “The radius and height of a cylinder are in the ratio 4:7. Find the diameter of the<br />cylinder if its volume is 1188cm³.​”

1. Answer:

   [tex]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

   \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[/tex]

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2. 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

   [tex]\sf \implies \dfrac{Radius}{ \: Height} \: = \: \dfrac{4}{7} [/tex]

   [tex]\sf \implies \: Height \: = \: \dfrac{7}{4} \times Radius[/tex]

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   Now ,

   Let radius = r

   ➝ Height = 7r/4

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   Volume of cylinder = π r² h

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

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

   [tex]\sf \implies \:1188 \: {cm}^{3} \: = \: \dfrac{11}{2} r^3[/tex]

   [tex]\sf \implies \: r^3 = 1188 \: {cm}^{3} \times \dfrac{2}{11} [/tex]

   [tex]\sf \implies \: r^3 = 108 \times 2 \: {cm}^{3} [/tex]

   [tex]\sf \implies \: r^3 = 216 \: {cm}^{3} [/tex]

   [tex]\sf \implies \: r^3 = \: {(6 \: cm )}^{3} [/tex]

   [tex]\sf \implies \: r = 6cm[/tex]

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   ➝ Diameter = 2r

   ➝ Diameter = 2(6 cm)

   ➝ Diameter = 12cm

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   ANSWER : 12 cm

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