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 .​

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

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

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${\bigstar {\boxed{\red{\bf{Given:-}}}}}$

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

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${\bigstar {\boxed{\red{\bf{Find:-}}}}}$

Glazed paper used on its outer surface and total cupboard and glazed paper used by the whole class = ?

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${\bigstar {\boxed{\red{\bf{Solution:-}}}}}$

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

$<font color="blue">$

= [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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$<font color="black">$

The amount of glazed paper required to cover the pen stand will be equal to the amount of cardboard used for making each pen stand.

Thus,

$<font color="blue">$

= [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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$<font color="black">$

The total cardboard and glazed paper used by the whole class consisting of 20 students is,

$<font color="blue">$

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

= 20 × [269.5 + 231]

= 20 × 500.5

= 10010 cm²

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