Question

The curved surface area and the volume of a
toy, cylindrical in shape, are 132 cm2 and
462 cm3 respectively. Find, its diameter and
its length.​

Answer 1

Answer:

Ur answer is here in this ATTACHMENT...

Step-by-step explanation:

Diameter of the toy = 14 cm

Height of the toy = 3 cm

Answer 2

GivEn:-

• Curved surface area of cylindrical toy = 132cm²

• Volume of cylindrical toy = 462cm³

To find:-

• Diameter of Cylindrical toy.

SoluTion:-

✩ Let the radius of the toy be r cm.

✩ And height of toy be h cm.

⋆ Reference of image is shown in diagram

$\setlength{\unitlength}{1cm}\begin{picture}(12,4)\thicklines\put(2.7,2.7){ . }\put(6,3){\circle{2}}\put(6,6){\circle{2}}\put(6,3){\line(0,1){3}}\put(5.3,3){\line(0,1){3}}\put(6.73,3){\line(0,1){3}}\put(6,3){\line(1,0){0.7}}\put(6,6){\line(1,0){0.7}}\put(6.2,6.13){ r }\put(6.8,4.5){ h }\end{picture}$

Now,

$\dag\;{\underline{\underline{\bf{\pink{According\;to\;question:-}}}}}$

GivEn that,

✇ Curved surface area of cylinder = 132cm²

As we know that,

$\dag\;{\underline{\boxed{\bf{\blue{C.S.A.\;of\;Cylinder = 2 \pi rh}}}}}$

$:\implies$ 2πrh = 132

$:\implies\sf r = \dfrac{132}{2 \pi h}\;\;\;...(1)$

Also,

✇ Volume of cylinder = 462 cm³

As we know that,

$\dag\;{\underline{\boxed{\bf{\blue{Volume\;of\; Cylinder = πr^2h}}}}}$

$:\implies$ πr²h = 462cm³

$:\implies\sf r^2 = \dfrac{462}{ \pi h}\;\;\;...(2)$

★ Now, Substituting value of r from eq(1) into eq(2) we get, -

$:\implies\sf \dfrac{(132)^2}{(2)^2 \times ( \pi)^2 \times (h)^2} = \dfrac{462}{ \pi h}$

$:\implies\sf 4 \times \pi \times h = \dfrac{132 \times 132}{462}$

$:\implies\sf h = \dfrac{132 \times 132}{462 \times \pi \times 4}$

$:\implies\sf h = \dfrac{132 \times 132 \times 7}{462 \times 22 \times h}$

$:\implies{\underline{\boxed{\bf{\purple{h = 3\;cm}}}}}$ ★

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★ Now Put the value of h in eq(1), we get

$:\implies\sf r = \dfrac{132 \times 7}{2 \times \22 \times 3}$

$:\implies{\underline{\boxed{\bf{\purple{r = 7\;cm}}}}}$ ★

$\therefore$ Diameter of the cylindrical toy = 2 × r

$:\implies\sf 2 \times 7 = 14\;cm$

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Additional Information:-

★ Formulas related to cylinder -

⠀⠀⠀✩ $\sf Lateral\;Surface\;Area\;of\;cylinder = 2 \pi rh$

⠀⠀⠀✩ $\sf Total\;Surface\;Area\;of\;cylinder = 2 \pi r[r + h]$

⠀⠀⠀✩ $\sf Volume\;of\;cylinder = \pi r^2h$

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