2019 · Q62
A solid metallic cylinder of height 10 cm and radius 6 cm is melted to make two cones in the ratio of volume 1:2 and of the same height as 10 cm. What is the percentage increase in the flat surface area?
Elementary MathematicsMensuration
- A25%
- B50%
- C75%
- D100%
Explanation
Cylinder volume 360.pi splits into cones of volume 120.pi and 240.pi (height 10), giving radii 6 and 6.sqrt(2). Flat (circular) area: cylinder 2.pi.x36 = 72.pi; cones pi.x36+pi.x72 = 108.pi. Increase = 36.pi/72.pi = 50%.