Let diameter, radius and height of first cone are d₁, r₁ and h₁, respectively and that of second cone are d₂, r₂ and h₂, respectively.
r₁/r₂ = d₁/d₂ = 3/5,
h₁/h₂ = ?
Given,
[(1/3)πr²₁h₁] / [(1/3)πr²₂h₂] = 1/3
⇒ (3/5)² x h₁/h₂ = 1/3

Correct Option: A

Let diameter, radius and height of first cone are d₁, r₁ and h₁, respectively and that of second cone are d₂, r₂ and h₂, respectively.
r₁/r₂ = d₁/d₂ = 3/5,
h₁/h₂ = ?
Given,
[(1/3)πr²₁h₁] / [(1/3)πr²₂h₂] = 1/3
⇒ (3/5)² x h₁/h₂ = 1/3
⇒ h₁/h₂ = (1/3) x (25/9) = 25/27

Given, l₁/l₂ = 5/7
Now, curved surface area of the first cone = π rl₁
and curved surface area of second cone = πrl₂

Correct Option: D

Given, l₁/l₂ = 5/7
Now, curved surface area of the first cone = π rl₁
and curved surface area of second cone = πrl₂
∴ Ratio = πrl₁/πrl₂ = l₁/l₂ = 5 : 7

Let the fixed height of a right circular cone is h and initial radius is r
Then, initial volume of cone, V₁ = (1/3)πr²h
After increasing 15% radius of a cone = (r + 3r/20) = 23r/20
New volume become, V₂ = (1/3)π(23/20)²r²h
∴ Increasing percentage = [(V₂ - V₁) / V₁] x 100

Correct Option: C

Let the fixed height of a right circular cone is h and initial radius is r
Then, initial volume of cone, V₁ = (1/3)πr²h
After increasing 15% radius of a cone = (r + 3r/20) = 23r/20
New volume become, V₂ = (1/3)π(23/20)²r²h
∴ Increasing percentage = [(V₂ - V₁) / V₁] x 100
= {[(1/3)πr²h] / [(1/3)πr²h]} {(23/20)² - 1} x 100
= (23/20 + 1)(23/20 - 1) x 100
= 43/20 x 3/20 x 100 = 32.25%

Let level of water will be increased by h cm
π x (15)² x h = (4/3)π(10)³

Correct Option: D

Let level of water will be increased by h cm
π x (15)² x h = (4/3)π(10)³
∴ h = [(4/3) x 10 x 10 x 10] / [15 x 15]
= 5²⁵/₂₇ cm

1 hec = 10000 m³
Volume of water = Base area x Height

Correct Option: C

1 hec = 10000 m³
Volume of water = Base area x Height
= (10000 x 10)/100 = 1000 m³