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A hollow hemispherical bowl is made of silver with its outer radius $18 cm$ and inner radius $14 cm$ respectively. The bowl is melted to form a solid right circular cone of radius $16 cm$ . Find the height of the cone.

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Important Questions on Geometry

MEDIUM

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

The radii of the frustum of a right circular cone are in the ratio

2 : 1

.What is the ratio of the volume of the frustum of the cone to that of the whole cone?

MEDIUM

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

A cylindrical vessel

60 c m

in diameter is partially filled with water. A sphere

30 c m

in diameter is gently dropped into the vessel and is completely immersed. To what further height will the water in the cylinder rise?

MEDIUM

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

From a solid cylinder whose height is

8 c m

and radius is

6 c m,

a conical cavity of height

8 c m

and base radius

6 c m

is formed by hollowing out. What is the inner surface area of the cavity?

EASY

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

The minute hand of the clock is

21 cm

long. What is the area of the face of the clock described by the minute hand between

10.10 am and 10.30 am

MEDIUM

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

A sector of radius

10.5 cm

with the central angle

120^{o},

is folded to form a cone by joining the two bounding radii of the sector. What is the volume (in

{cm}^{3}

) of the cone so formed?

MEDIUM

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

A tent has been constructed which is in the form of a right circular cylinder surmounted by a right circular cone, whose axis coincides with the axis of the cylinder. If the radius of the base of the cylinder is

50 m

, the height of the cylinder is

10 m

and the total height of the tent is

15 m,

then what is the capacity of the tent in cubic metres?

MEDIUM

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

A cylinder of height

2 x

is circumscribed by a sphere of radius

2 x

such that the circular ends of the cylinder are two small circles on the sphere. What is the ratio of the curved surface are of the cylinder to the surface area of the sphere?

EASY

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

ABCD

is a cyclic quadrilateral. The bisectors of the anlges

A, B, C,

and

D

cut the circle at

P, Q, R,

and

S

respectively. What is

∠ PQR + ∠ RSP

equal to?

HARD

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

Consider two equivalent, triangular hollow prisms A and B made of thin glass plates and arranged with negligible spacing as shown in the figure. A beam of white light is incident on prism A from the left. Given that, the refractive index of water is inversely related to temperature, the beam to the right of prism B would not appear white, if

Question Image

EASY

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

In the figure given below, $M$ is the mid-point of $A B and ∠ D A B = ∠ C B A and ∠ A M C = ∠ B M D$ . Then the triangle $A D M$ is congruent to the triangle $B C M$ by______.

Question Image

EASY

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

The length and breadth of a room are

21 m and 16 m

respectively. If the length of the longest rod that can be placed in the room is

29 m

, then what is the height of the room?

MEDIUM

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

A solid sphere of diameter

17.5

c m

is cut into two equal halves. What will be the increase (in

c m^{2}

) in the total surface area?

EASY

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

What is the area of the right-angled triangle, if the radius of the circumcircle is

5 cm

and altitude drawn to the hypotenuse is

4 cm

MEDIUM

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

Two rectangular sheets of sizes

2 π \times 4 π

square unit and

π \times 5 π

square unit are available. A hollow right circular cylinder can be formed by joining a pair of parallel sides of any sheet. What is the maximum possible volume of the circular cylinder that can be formed this way?

EASY

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

In a quadrilateral

ABCD,

∠ B = 90 °

and

{AB}^{2} + {BC}^{2} + {CD}^{2} - {AD}^{2} = 0

, then what is

∠ ACD

equal to?

EASY

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

If the sum of all interior angle of a regular polygon is twice the sum of its all external angle then the polygon is______.

EASY

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

Consider the following statements:

$1 .$ The diagonals of a trapezium divide each other proportionally.

$2 .$ Any line drawn parallel to the parallel sides of a trapezium, divides the non-parallel sides proportionally.

Which of the above statements is/are correct?

EASY

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

A hollow cube is formed by joining six identical squares. A rectangular cello tape of length

4 cm

and breadth

0.5 cm

is used for joining each pair of edges. What is the total area of cellotape used?

MEDIUM

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

The radius of a sphere is reduced by

40 %

. By what percent will its volume decrease?

EASY

Quantitative Abilities>Geometry>Geometry>3D Geometrical Shapes

The total surface area of a hemisphere is

1039.5 c m^{2}

. Find its diameter (in

c m

.).

A hollow hemispherical bowl is made of silver with its outer radius 18 cm and inner radius 14 cm respectively. The bowl is melted to form a solid right circular cone of radius 16 cm. Find the height of the cone.

Important Questions on Geometry

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A hollow hemispherical bowl is made of silver with its outer radius $18 cm$ and inner radius $14 cm$ respectively. The bowl is melted to form a solid right circular cone of radius $16 cm$ . Find the height of the cone.