Geometry

Surface Area

Surface Area: Level 2 Challenges

         

In a spherical ball, a large number of dimples have been carved. The shape of these dimples is part of a sphere.

Is it possible for the dimpled ball to have a smaller surface area than it had before the dimples were carved?

The edge of a cube is increased by 20%20 \%. What is the percentage increase in its surface area?

Two equivalent regular hexagonal-based prisms are divided and rearranged into 3 equilateral triangular-based prisms, as shown above. After rearrangement, the total surface area of all prisms has increased by 12.5% with the constant height.

If the height of each prism is 3 cm\sqrt{3} \text{ cm}, what is the side length of the regular hexagon base in cm\text{cm}?

A spherical orange is cut about the vertical axis into 8 equal slices as shown above.

What is the ratio of the total surface area of the 8 slices to that of the original orange?

If a cuboid of dimensions 10 cm×15 cm×5 cm 10 \text{ cm} × 15 \text{ cm}× 5 \text{ cm} is cut to form cubes of sides 5 cm, then what is the difference between the sum of the surface areas of these cubes and the surface area of the original cuboid?

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