Question

In a SUPW class, 20 student made pen stand of cupboard. the base of the pen stand is a circle with radius 3.5 cm and height of the pen stand is 10.5 cm .find how much cupboard was used by each. how much glazed paper is used on its outer surface also find the total cupboard and glazed paper used by the whole class .​
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Answer 1

${\huge {\underline {\mathfrak {\red {Answer}}}}}$

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No. of students in the SUPW class = 20

The radius of the base of the pen stand, r = 3.5 cm

The height of the pen stand, h = 10.5 cm

Thus,

Total cardboard required to make one pen stand is given by,

= [CSA of a cylinder] + [CSA of base of pen stand]

= [2πrh] + [πr²]

= πr [2h + r]

= (22/7) * 3.5 * [(2*10.5) + 3.5]

= (22/7) * 3.5 * 24.5

= 269.5 cm²

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Thus,

Glazed paper used on the outer curved surface of the pen stand (neglecting the base area) is given by,

= [Cardboard required to make one pen stand] – [Area of the base of the pen stand]

= 269.5 – [π²]

= 269.5 – [(22/7) * (3.5)²]

= 269.5 – 38.5

= 231 cm²

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= 20 * [(Total cardboard used for each pen stand) + (Total glazed paper used on the outer curved surface of each pen stand)]

= 20 * [269.5 + 231]

= 20 * 500.5

= 10010 cm²

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Answer 2

AnswEr :

• Radius = 3.5 cm
• Height = 10.5 cm

Pen Stand will must be Open from Top. So it's just got CSA and Bottom of Cylinder.

$\underline{\bigstar\:\textsf{Area of 1 Pen Stand made by 1 Student:}}$

$:\implies\texttt{Area = (CSA + Bottom Area) of Cylinder}\\\\\\:\implies\tt Area =2\pi rh + \pi r^2\\\\\\:\implies\tt Area =\pi r(2h + r)\\\\\\:\implies\tt Area =\dfrac{22}{7} \times 3.5(2 \times 10.5+3.5)\\\\\\:\implies\tt Area =11(21+3.5)\\\\\\:\implies\tt Area =11 \times 24.5\\\\\\:\implies \underline{\boxed{\tt Area =269.5\:cm^2}}$

⠀

$\therefore\:\underline{\textsf{One Student will use \textbf{269.5 cm ^2 } of cupboard}}.$

$\rule{200}{2}$

$\underline{\bigstar\:\textsf{Glazed Paper Used by 1 Student :}}$

$:\implies\tt Glazed\:Paper= CSA\:of\: Cylinder\\\\\\:\implies\tt Glazed\:Paper=2\pi rh\\\\\\:\implies\tt Glazed\:Paper=2 \times\dfrac{22}{7} \times3.5 \times 10.5\\\\\\:\implies\tt Glazed\:Paper=22 \times 10.5\\\\\\:\implies\tt Glazed\:Paper=231\:cm^2$

$\rule{150}{1}$

$\underline{\bigstar\:\textsf{Total Usage by Whole Class :}}$

$\dashrightarrow\:\:\tt Total=Students\times (Cupboard+Glazed\:Paper)\\\\\\\dashrightarrow\:\:\tt Total=20 \times (269.5\:cm^2+231\:cm^2)\\\\\\\dashrightarrow\:\:\tt Total=20 \times 500.5\\\\\\\dashrightarrow\:\:\underline{\boxed{\tt Total=10010\:cm^2}}$

⠀

$\therefore\:\underline{\textsf{Total Usage by whole class is \textbf{10010 cm ^2 }}}.$