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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 of a Cuboid

         

In the diagram above shows a cuboid with \(x=6, y=3,\) and \(z=4.\) Find the surface area of the cuboid.

Note: The above figure is not drawn to scale.

The above diagram shows a large cuboid with a smaller cuboid cut off from the corner. If \(\alpha=6, \beta=3,\) \(\gamma=6,\) \(x=11, y=6,\) and \(z=12,\) what is the surface area of the remaining body?

Note: The above figure is not drawn to scale.

The cuboid in the above diagram is to be tiled by square-shaped tiles on all six faces of the cuboid. If \(x=10\) cm, \(y=4\) cm, \(z=4\) cm, and the side length of each tile is \(2\) cm, how many tiles are needed?

Note: A tiling is a non-overlapping arrangement of tiles covering the entire surface area with no gaps. The above figure is not drawn to scale.

What is the surface area of a cube inscribed in a sphere with radius \(6,\) as shown in the above diagram?

The volume of the cuboid shown in the above diagram is \(56.\) If \(x=7\) and \(y=2,\) what is the surface area of the cuboid?

Note: The above figure is not drawn to scale.

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