Geometry

Solids

Medium

A flask in the shape of a right circular cone of height 36 cm is completely filled with tea. The tea is then poured into another right circular cylindrical flask whose radius is two-third of the radius of base of the circular cone. Then, the height of the tea in the cylindrical flask is

27 cm

42 cm

72 cm

24 cm

✅ Correct Option: 1

A flask in the shape of a right circular cone of height 36 cm is completely filled with tea. The tea is then poured into a cylindrical flask whose radius is two-third of the radius of the base of the cone.

Let the radius of the conical flask be $r$ and the radius of the cylindrical flask be $R = \frac{2r}{3}$ .

Let the height of tea in the cylindrical flask be $H$ .

The volume of tea remains constant when poured from one flask to another.

Volume of cone $= \frac{1}{3}\pi r^2 h$

$= \frac{1}{3} \times \pi \times r^2 \times 36$

$= 12\pi r^2$

Volume of cylinder $= \pi R^2 H$

$= \pi \times \left(\frac{2r}{3}\right)^2 \times H$

$= \pi \times \frac{4r^2}{9} \times H$

$= \frac{4\pi r^2 H}{9}$

Since the volume of tea remains the same:

$12\pi r^2 = \frac{4\pi r^2 H}{9}$

$12 = \frac{4H}{9}$

$108 = 4H$

$H = 27$

Therefore, the height of tea in the cylindrical flask is 27 cm.

2025: 13 May Shift 2

Read the information given carefully and answer the question that follows:

(A) 72 kmph = 20 m/s

(B) 25 m/s = 80 kmph

(D) Volume of a Cube of edge length $a$ is $a^3$

Choose the correct answer from the options given below:

2026: 26 May Shift 1

Consider the surface area of the following solids.

(A) A cube of edge 8 cm.

(B) A cylinder with a diameter of base 10 cm and height 42 cm.

(D) A sphere with a radius 21 cm.

Arrange the above in decreasing order.

Choose the correct answer from the options given below:

2022: 6 Oct Shift 1

If each side of a cube is reduced by 50%, the surface area will reduced by.

2025: 27 May Shift 1

If the slant height of a cone is decreased by 15 percent and the radius of its base is increased by 20 percent, then by what percent will its curved surface area change?

2026: 25 May Shift 2

The surface area of a cube is 1734 $cm^2$ , its volume is :

2026: 25 May Shift 1

Find the surface area of a sphere of radius 10.5 cm?

A flask in the shape of a right circular cone of height 36 cm is completely filled with tea. The tea is then poured into another right circular cylindrical flask whose radius is two-third of the radius of base of the circular cone. Then, the height of the tea in the cylindrical flask is

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