Geometry

Surface Area

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 NπN \pi, what is the value of NN?

Brilli the ant is playing with a ball of radius RR, which is a positive integer. Given that the surface area and volume of the ball are NπN\pi and MπM\pi, where NN and MM are 4-digit integers, what is RR?

Details and assumptions

The number 12=01212=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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