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​

Answer 1

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

Answer 2

Answer:

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

________________________

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

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

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

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

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

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

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

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

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

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

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

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

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

_______________________

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

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

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

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

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