Arrange the volumes of the following geometrical figures in decreasing order of their value.
A. A cuboid of length 5 cm, breadth 3 cm and height 4 cm.
B. A cube on each side of 4 cm.
C. A cylinder of radius 3 cm and length 3 cm.
D. A sphere of radius 3 cm.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → D, C, B, A
Each volume is worked out from its standard formula, taking \(\pi\approx3.14\), and the four values are then compared. The two round solids, which carry the factor \(\pi\), come out larger than the cube and the cuboid here.
A. Cuboid — \(60\,\mathrm{cm^3}\), the smallest
length \(\times\) breadth \(\times\) height \(=5\times3\times4\)
B. Cube — \(64\,\mathrm{cm^3}\)
side3 \(=4^3\)
C. Cylinder — about \(84.8\,\mathrm{cm^3}\)
\(\pi r^2h=\pi\times9\times3=27\pi\)
D. Sphere — about \(113.1\,\mathrm{cm^3}\), the largest
\(\frac{4}{3}\pi r^3=\frac{4}{3}\pi\times27=36\pi\)