2 points 65. The radius and height of a cylinder are in the ratio 3:2 and its volume is 19,404 cm” then its radius is

Question

2 points
65. The radius and height of a
cylinder are in the ratio 3:2 and
its volume is 19,404 cm” then
its radius is
O a)7cm​

in progress 0
Eliza 4 weeks 2021-08-15T08:30:02+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-15T08:31:31+00:00

    Answer:

    Let the radius be 3x and height be 2x.

    ________________________

    \underline{\boldsymbol{According\: to \:the\: Question\:now :}}

    : \implies \sf Volume  \: of \:  cylinder = \pi r^2h \\  \\  \\

    : \implies \sf 19404 =   \pi  {r}^{2} h \\  \\  \\

    : \implies \sf 19404 = \pi (9x^{2})(2x) \\  \\  \\

    : \implies \sf 19404 = 18\pi x ^{3} \\  \\  \\

    : \implies \sf 19404 = 18 \times  \dfrac{22}{7} \times   x ^{3} \\  \\  \\

    : \implies \sf 19404 \times  \dfrac{7}{22} = 18x^{3}    \\  \\  \\

    : \implies \sf 882 \times 7= 18 x^{3} \\  \\  \\

    :\implies \sf 6174= 18 x^{3} \\  \\  \\

    : \implies \sf x^{3}  = \dfrac{6174}{18} \\  \\  \\

    : \implies \sf x^{3} = 343 \\  \\  \\

    : \implies \underline{\boxed{\sf x = 7 \: cm}}\\  \\  \\

    \therefore\:\underline{\textsf{Radius of cylinder is 3x = 3(7)  = \textbf{21 cm}}}. \\

    _______________________

    \boxed{\bf{\mid{\overline{\underline{\bigstar\: Extra\: Brainly \: Knowledge :}}}}\mid}\\\\

    \boxed{\bigstar{\sf \ Cylinder :- }}\\ \\\sf {\textcircled{\footnotesize1}} Volume \ of \ Cylinder= \pi r^2 h \\ \\ \\ \sf {\textcircled{\footnotesize2}}\ Curved \ surface\ Area \ of \ cylinder= 2\pi r h\\ \\ \\ \sf {\textcircled{\footnotesize3}} Total \ surface \ Area \ of \ cylinder= 2\pi r (h+r)

    \boxed{\bigstar{\sf \ Cone :- }}\\ \\\sf {\textcircled{\footnotesize1}} Volume \ of \ Cone= \dfrac{1}{3}\pi r^2 h \\ \\ \\ \sf {\textcircled{\footnotesize2}}\ Curved \ surface\ Area \ of \ Cone = \pi r l \\ \\ \\ \sf {\textcircled{\footnotesize3}} Total \ surface \ Area \ of \ Cone = \pi r (l+r) \\ \\ \\ \sf {\textcircled{\footnotesize4}} Slant \ Height \ of \ cone (l)= \sqrt{r^2+h^2}

    \boxed{\bigstar{\sf \ Hemisphere :- }}\\ \\\sf {\textcircled{\footnotesize1}} Volume \ of \ Hemisphere= \dfrac{2}{3}\pi r^3 \\ \\ \\ \sf {\textcircled{\footnotesize2}}\ Curved \ surface\ Area \ of \ Hemisphere = 2 \pi r^2 \\ \\ \\ \sf {\textcircled{\footnotesize3}} Total \ surface \ Area \ of \ Hemisphere = 3 \pi r^2

    \boxed{\bigstar{\sf \ Sphere :- }}\\ \\\sf {\textcircled{\footnotesize1}} Volume \ of \ Sphere= \dfrac{4}{3}\pi r^3 \\ \\ \\ \sf {\textcircled{\footnotesize2}}\ Surface\ Area \ of \ Sphere = 4 \pi r^2

    0
    2021-08-15T08:31:40+00:00

    Given :-

    • The radius and height of a cylinder are in the ratio 3:2 and its volume is 19,404 cm³

    To find :-

    • Radius of cylinder

    Solution :-

    • Radius and height of cylinder in ratio = 3 : 2
    • Volume of cylinder = 19404cm³

    Let the radius be 3x and height be 2x

    As we know that

    → Volume of cylinder = πr²h

    Where ” r ” is radius, ” h ” is height of a cylinder

    According to question

    → Volume of cylinder = 19404

    → πr²h = 19404

    → 22/7 × (3x)² × 2x = 19404

    → 22/7 × 9x² × 2x = 19404

    → 22/7 × 18x³ = 19404

    → 22 × 18x³ = 19404 × 7

    → 396x³ = 135828

    → x³ = 135828/396

    → x³ = 343

    → x = ∛343

    → x = 7

    Hence,

    • Radius of cylinder= 3x = 21cm

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