"Question 11 The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?
Class 9 - Math - Surface Areas and Volumes Page 217"
Answers
Height of the penholder (h) = 10.5cm
Cardboard required by 1 competitor = CSA of one penholder + area of the base
= 2πrh + πr2
= [(2 × 22/7 × 3 × 10.5) + 22/7 × 32] cm2
= (198 + 198/7) cm2
= 1584/7 cm2
Cardboard required for 35 competitors = (35 × 1584/7) cm2
= 7920 cm2
Right Circular cylinder:
Right circular cylinder is generated by revolution of a rectangular sheet about one of its side so the area of a rectangular sheet gives us the curved surface area of the cylinder and length of the rectangular sheet is equal to the circumference of the circular base.
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Given:
Radius of the penholder (r) = 3cm
Height of the penholder (h) = 10.5cm
Cardboard required by 1 competitor = CSA of one
penholder + area of the base= 2πrh +πr²
= [(2 × 22/7 × 3 × 10.5) +( 22/7 ×3²)]
= (198 + 198/7)
= 1584/7 cm²
Cardboard required for 35 competitors = (35 ×
1584/7)
= 7920 cm²
Hence, 7920 cm² of cardboard was required to be bought for the competitors.
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Hope this will help you...