A games shop sells marbles in clear plastic cylinders. Four marbles fit across the diameter of the cylinder, and 10 marbles fit from the base to the top of the cylinder. Each marble has a diameter of 2cm2cm. What is the area of the plastic that is needed to nake one cylinder?

rocedwrp

rocedwrp

Answered question

2021-02-10

A games shop sells marbles in clear plastic cylinders. Four marbles fit across the diameter of the cylinder, and 10 marbles fit from the base to the top of the cylinder. Each marble has a diameter of 2cm2cm. What is the area of the plastic that is needed to nake one cylinder?

Answer & Explanation

Corben Pittman

Corben Pittman

Skilled2021-02-11Added 83 answers

The total surface area of a cylinder is given by:
S=2πr2+2πrh
Since 4 marbles fit across the diameter of the cylinder and each marble has a diameter of 2 cm, the diameter of the cylinder is 4(2)=8. So, r=82=4 cm. Since 10 marbles fit from the base to the top of the cylinder and each marble has a diameter of 2 cm, the height of the cylinder is h=10(2)=20 cm. So, the area is:
S=2π(4)2+2π(4)(20)

S=32π+160π
S=192π cm2603.2 cm2

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