The radius and height of a cylinder are in the ratio 4:7. Find the diameter of thecylinder if its volume is 1188cm³. About the author Margaret
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] Reply
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] ________________________________ Now , Let radius = r ➝ Height = 7r/4 ________________________________ 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] ________________________________ ➝ Diameter = 2r ➝ Diameter = 2(6 cm) ➝ Diameter = 12cm ________________________________ ANSWER : 12 cm Reply
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]
Given :
To find :
Diameter of cylinder
Formula used:
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