12. In a SUPW dass. 20 students made pen stands of
cardboard. 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 cardboard was used by each. How much glazed paper
Is used on its outer curved surface? Also find the total cardboard
and glazed paper used by the whole class.
Answers
The cardboard used by each student was 269.5 cm².
The glazed paper Is used on its outer curved surface is 231 cm².
The total cardboard and glazed paper used by the whole class is 10010 cm².
Step-by-step explanation:
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
Step 1: Finding the cardboard used by each student
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
Step 2: Finding the glazed paper used in the outer curved surface of a pen stand
We know that 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,
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
Step 3: Finding the total cardboard and glazed paper used by the whole class
The total cardboard and glazed paper used by the whole class consisting of 20 students is,
= 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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Also View:
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