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Surface Area

A spherical balloon is inflated until its volume becomes 27 times its original volume. How much does its surface area increase?

Surface Area - Problem Solving

         

The volume of a cube with positive side length is numerically equal to the surface area of a cube (though they will have different units). What is the volume of the cube?

The surface area of a sphere of radius 1 is equal to the surface area of a cylinder with a circular base of radius 1. What is the height of the cylinder?

The volume of a sphere is numerically equal to the surface area of the sphere. If this value is equal to \(N \pi\), what is the value of \(N\)?

Brilli the ant is playing with a ball of radius \(R\), which is a positive integer. Given that the surface area and volume of the ball are \(N\pi \) and \(M\pi\), where \(N\) and \(M\) are 4-digit integers, what is \(R\)?

Details and assumptions

The number \(12=012\) is a 2-digit number, not a 3-digit number.

If the surface area of a sphere is numerically equal to the volume of the sphere, what is the radius?

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