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Question
The height of a circular cylinder is 4.2cm. There times the sum of the areas of its two circular faces is twice the area of the curved surface. Find the volume of the cylinder correct to 1 decimal place.
Solution
Height of the cylinder (h) = 4.2cm
Let r be the radius of the cylinder
Sum of the area of 2 circular faces = πr2 + πr2
Curved surface area of cylinder = 2π rh
Given that:
3 x (πr2 + πr2) = 2 x 2π rh
6πr2 = 4π rh
6r = 4h
6r = 4 x 4.2
r = `(16.8)/(6)`
r = 2.8cm
∴ Volume of the cylinder
= π x r2 x h
= `(22)/(7) xx 2.8^2 xx 4.2`
= 103.5cm3.
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