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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. 628 cm2
2. 314 cm2
3. 289 cm2
4. 356 cm2

Correct answer: 314 cm2

Solution

For the cube, lateral surface area = \(4a^2\), and since side \(a=R\), it is \(4R^2\). For the cylinder, lateral surface area = \(2\pi rh = 2\pi(R)(2R)=4\pi R^2\). Their difference is 420, so \(4\pi R^2 - 4R^2 = 420\), giving \(R\approx 7\) using \(\pi=\frac{22}{7}\). Then the required area is \(\pi(R+3)^2 = \pi(10)^2 = 100\pi \approx 314\text{ cm}^2\).

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