Arrange the following three-dimensional objects in the descending order of their volumes:
i. A cuboid with dimensions 10 cm, 8 cm and height 5 cm
ii. A cube of side 9 cm
iii. A cylinder with base radius 7 cm and height 7 cm
iv. A sphere of radius 7 cm
A. (i), (ii), (iii), (iv)
B. (iv), (iii), (ii), (i)
C. (iii), (iv), (i), (ii)
D. (iv), (iii), (i), (ii)
GATE 2018 · General Aptitude · Geometry · medium
Answer: Descending order: (iv) sphere, (iii) cylinder, (ii) cube, (i) cuboid — Option B
Volume of cuboid (i): V_i = 10 × 8 × 5 = 400 cm^3
Volume of cube (ii): V_ii = 9^3 = 729 cm^3
Volume of cylinder (iii): V_iii = pi × 7^2 × 7 = 343 pi ≈ 1077.6 cm^3
Volume of sphere (iv): V_iv = (4/3) pi × 7^3 = (4/3) × 343 pi ≈ 1436.8 cm^3
Rank descending: 1436.8 > 1077.6 > 729 > 400 => order is (iv), (iii), (ii), (i)