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The lateral surface area of a cube is 420 cm² less than the lateral surface area of a cylinder. The height of the cylinder is 2R cm and its radius is R cm. If the side of the cube is equal to the radius of the cylinder, find the approximate area of a circle whose radius is (R + 3) cm.

1. 314 cm2
2. 340 cm2
3. 388 cm2
4. 225 cm2

Correct answer: 314 cm2

Solution

The cube's lateral surface area is $4R^2$ and the cylinder's lateral surface area is $2\pi R(2R)=4\pi R^2$. Their difference is 420, which gives $R$ approximately 7 when using $\pi=\frac{22}{7}$. Then the circle radius is $R+3=10$, so area is about $\pi\times 10^2=314$ cm².

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