What is the height (in m) of a conical water tank having radius of 70 m and volume of 46,200 m³? (Take π = 22⁄7)

Correct — D. Start from the cone's volume formula and make h the subject.

V = 1⁄3 πr²h
46,200 = 1⁄3 × 22⁄7 × 70² × h

70² = 4900, and 22⁄7 × 4900 = 15,400
So 46,200 = 15,400h ⁄ 3

h = 46,200 × 3 ⁄ 15,400
= 1,38,600 ⁄ 15,400 = 9 m → option (d).

Why the others are wrong

• (a)
  27 — Three times the answer, which is what applying the ⅓ in the wrong direction gives. A cone 27 m tall on a 70 m radius would hold 1,38,600 m³, three times the volume stated.
• (b)
  54 — A height of 54 m would hold 2,77,200 m³ — six times the 46,200 m³ the question gives. The base area 15,400 m² makes each extra metre of height worth 5,133⅓ m³.
• (c)
  18 — A height of 18 m would hold 92,400 m³, exactly twice the stated volume. The arithmetic 46,200 × 3 ⁄ 15,400 comes to 9, and doubling it has no basis in the formula.

A cone holds one third of the cylinder standing on the same base with the same height: V = 1⁄3 πr²h.

Rearranged for the unknown, h = 3V ⁄ (πr²). The numbers are built so no decimals survive: r = 70 gives r² = 4900, and 22⁄7 × 4900 = 15,400 exactly.

From there h = 3 × 46,200 ⁄ 15,400 = 1,38,600 ⁄ 15,400 = 9. Every wrong option is a whole multiple of 9, so what is being tested is where the 3 belongs, not the multiplication.

Key facts

• Volume of a cone = 1⁄3 πr²h, one third of the cylinder on the same base and height.
• Rearranged for height, h = 3V ⁄ (πr²).
• With r = 70 m and π = 22⁄7, the base area πr² is exactly 15,400 m².
• 3 × 46,200 = 1,38,600, and 1,38,600 ⁄ 15,400 = 9 m.

Common traps

• Using the cylinder formula V = πr²h and dropping the ⅓, which returns h = 3 m.
• Applying the factor 3 a second time after isolating h, which lands on 27 m.
• Reading the 70 m as a diameter, which would change r² from 4900 to 1225.

No directly related past PYQ was found.