Question

The adjacent sides of the right-angle triangle are 5 cm and 12 cm respectively. Using the longer side of the triangle as the axis we form a right circular cone by fully rotating the triangle along its axis. Now, if we fill a right circular cylindrical container. whose radius is 5 cm, using the cone as a mug thrice with water, then what would be the height of the water in the container in centimeters.​

Answer 1

Given :-

• sides of the right-angle triangle are 5 cm and 12 cm respectively.
• Rotated Along Longest side.
• Radius of container is 5cm.
• Volume of container is 3 times of volume of mug.

To Find :-

• Height of water in The container ?

Concept Used :-

• Pythagoras Theoram .
• when Rotated Along longest sides of Hypotenuse of Right ∆, Height of cone becomes Hypotenuse of Right Angle ∆.
• Radius of cone so formed becomes (P*B/H).
• Volume of cone = (1/3) * π * r² * h .
• Volume of cylinder = π * R² * H .

Solution :-

❁❁ Refer To Image First .. ❁❁

we Have :-

→ P = 5

→ B = 12

→ H = √(5)² + (12)²

→ H = √25 + 144

→ H = √169

→ H = 13cm. = Height of cone so Formed .

And,

→ Radius of cone so formed = (12*5/13) = (60/13) cm.

So,

→ Volume of cone so Formed = (1/3) * π * (60/13)² * 13 ---------- Equation (1).

_______________________

Now, we have given that, Volume of container is 3 times of volume of mug & radius of container is 5cm.

So,

→ Volume of container = 3 * Volume of cone so formed .

→ π * (5)² * H = 3 * Volume of cone so formed

Putting value from Equation (1) now,

→ π * (5)² * H = 3 * [ (1/3) * π * (60/13)² * 13 ]

→ π * (5)² * H = π * (60/13)² * 13

π will be cancel from both sides

→ 25 * H = (60 * 60) / 13 .

→ H = (3600) / (25*13)

→ H = 11.07cm.

Hence, Height of cylindrical container or, the water in the container is upto Height of 11.07cm.