34. A sheet of rectangular paper measures 20 cm by 15 cm. It can be rolled up 2018side to form two cylinders, A and B as shown.A20B115(1) Which cylinder has a greater volume? How much more than the other?(ii) Suppose the sheet is divided into two equal parts, X andY, as shown and then rolled up to form two cylinders ofХheight 15 cm each. Would the sum of the volumes of thesetwo small cylinders be greater than the volume of cylinderΥ.B? Explain how you arrived at your conclusion.
Answers
1125/π cm³ , 1500/π cm³ , 750/π cm³
Step-by-step explanation:
A sheet of rectangular paper measures 20 cm by 15 cm
Height = 20 cm
Then Circumference of base = 15 cm
Radius of base = 15/2π
Volume = πr²h = π ( 15/2π)² * 20
= 1125/π cm³
Height = 15 cm
Then Circumference of base = 20 cm
Radius of base = 20/2π = 10/π
Volume = πr²h = π ( 10/π)² * 15
= 1500/π cm³
Divided into two parts
Height = 15 cm Circumference of base = 10
Radius of base = 10/2π = 5/π
Volume of one cylinder = πr²h = π ( 5/π)² * 15
= 375/π cm³
Volume of both cylinder = 2 * 375/π = 750/π cm³
No , Sum of the volumes of these two small cylinders not be greater than the volume of cylinder
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