Consider the volumes of the following:
(A) A cylinder with a radius of base 7 cm and height 10 cm.
(B) A cone of radius 7 cm and height 9 cm.
(C) A sphere of radius 6 cm.
The volumes of these figures in decreasing order shall be:
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A), (C), (B)
The volumes are found with the standard formulas: cylinder \(\pi r^2h\), cone \(\frac{1}{3}\pi r^2h\) and sphere \(\frac{4}{3}\pi r^3\), taking \(\pi=\frac{22}{7}\).
(A) A cylinder with a radius of base 7 cm and height 10 cm. — \(\frac{22}{7}\times7\times7\times10=1540\,\mathrm{cm^3}\), the largest of the three.
(C) A sphere of radius 6 cm. — \(\frac{4}{3}\times\frac{22}{7}\times6\times6\times6=\frac{6336}{7}\approx905\,\mathrm{cm^3}\).
(B) A cone of radius 7 cm and height 9 cm. — \(\frac{1}{3}\times\frac{22}{7}\times7\times7\times9=462\,\mathrm{cm^3}\), the smallest; a cone holds only one-third of a cylinder of the same base and height.