Multiple choice

What is the difference in the volume (in cm3 ) of a sphere of radius 7 cm and that of a cone of radius 7 cm and height 10 cm ? (Use π=22/7)

  1. 205

  2. 704

  3. 924

  4. 1078

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sphere volume = (4/3) × (22/7) × 7³ = (4/3) × (22/7) × 343 = 1,432 2/3 cm³. Cone volume = (1/3) × (22/7) × 7² × 10 = (1/3) × 22 × 7 × 10 = 1,540 1/3 cm³. Wait: let me recalculate. Cone = (1/3) × (22/7) × 49 × 10 = 1,540 cm³ (exactly since 49 cancels with 7). Sphere = (4/3) × 22 × 49 = (4/3) × 1,078 = 1,437 1/3. Difference = 1,540 - 1,437 1/3 = 102 2/3. This doesn't match options. Let me recalculate: (4/3) × (22/7) × 343 = 4,312/3 = 1,437.33. Cone = (1/3) × (22/7) × 49 × 10 = 10,780/21 = 513.33? No, (22/7) × 49 = 154, then × 10 = 1,540, then ÷ 3 = 513.33. So sphere - cone = 1,437.33 - 513.33 = 924.