Q.1.

If the volume of the cube is 729 cm3, then the surface area of the cube will be

Q.2.

Find the area of a square, one of whose diagonals is 3.8 m long.

Q.3.

The volume of a rectangular solid is to be increased by 50% without altering its base. To what extent the height of the solid must be changed.

Q.4.

Find the volume (in cub.cm) of a hemisphere of diameter 28 cm.

 

Q.5.

If the base of a pyramid is a square of 6cm side and its slant height is 5cm. Find its slant surface area.

Q.6.

A regular triangular pyramid is cut by 2 planes which are parallel to its base. The planes trisects the altitude of the pyramid. Volume of top, middle and bottom part is V1, V2 and V3 respectively. What is the value of V1 :V2 : V3?

Q.7.

If radius and height of a cylinder increase by 20% and15% respectively. then what is the % change in curved surface area?

Q.8.

Consider the following statements:

1) The perimeter of a triangle is greater than the sum of its three medinas.

2) In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD.

Which of the above statements is/are correct?

Q.9.

How many cubes of 3cm edge can be cut out of a cube of 18cm edge

Q.10.

A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is:

Q.11.

In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

Q.12.

Find the surface area of a10cm x 4cm x 3cm brick

Q.13.

An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is:

Q.14.

Find the area and circumference of a circle if the radius is 14 cm. (Take pi = 22/7)

 

Q.15.

Consider the following statements:

1) The number of circles that can be drawn through three non-collinear points is infinity.

2) Angle formed in minor segment of a circle is acute.

Which of the above statements is/are correct?

Q.16.

The volume of a hemisphere is 89.83 cm³. Find its diameter (in cm).

 

Q.17.

A cuboid of dimension 24cm x 9cm x 8 cm is melted and smaller cubers are of side 3 cm is formed.find how many such cubes can be formed ?

Q.18.

A single pipe of diameter x has to be replaced by six pipes of diameters 12 cm each. The pipes are used to covey some liquid in a laboratory. If the speed/flow of the liquid is maintained the same then the value of x is ?

Q.19.

The surface area of a cube is 1734 sq. cm. Find its volume

Q.20.

The dimensions of an open box are 50 cm, 40 cm and 23 cm. Its thickness is 2 cm. If 1 cubic cm of metal used in the box weighs 0.5 gms, find the weight of the box.

Q.21.

Water flows into a tank 200 m x 160 m through a rectangular pipe of 1.5m x 1.25 m @ 20 kmph . In what time (in minutes) will the water rise by 2 meters?

Q.22.

What is the ratio between the volumes of a cylinder and cone of the same height and of the same diameter

Q.23.

The curved surface area of a cylindrical pillar is 264 sq.m and its volume is 924 cub.m. Find the ratio of its diameter to its height

Q.24.

The ratio between the perimeter and the breadth of a rectangle is 5 :If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?

Q.25.

The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?

Q.26.

What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?

Q.27.

The areas of three consecutive faces of a cuboid are 12 cm², 20cm² and 15 cm², then the volume (in cm³) of the cuboid is

Q.28.

How many meshes are there in 1 squrare meter of wire gauge if each mesh is 8mm long and 5mm wide ?

Q.29.

Find the ratio of the surfaces of the inscribed and circumscribed spheres about a cube.

Q.30.

If each edge of a cube is increased by 50%, find the percentage increase in Its surface area

Q.31.

The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 cu. meters. Find the breadth of the wall.

Q.32.

The total surface area of a cube is 253.5 sq.cm. Find its side (in cm).

 

Q.33.

The cost of the paint is rs.36.50 per kg. if 1kg of paint covers 16sq.ft, how much will it cost to paint outside of a cube having 8 feet each side

Q.34.

Find the volume (in cm3) of a cube of side 6.5 cm.

 

Q.35.

Find the  surface area of a cuboid 16 m long, 14 m broad and 7 m high

Q.36.

One side of a triangle has length 8 and a second side has lengthWhich of the following could be the area of the triangle?

Q.37.

The volume of a hemisphere is 2425.5 cm³. Find its diameter (in cm).

 

Q.38.

Consider the following inequalities in respect of any triangle ABC:

1) AC –AB < BC

2) BC –AC < AB

3) AB –BC < AC

Which of the above are correct?

Q.39.

Choose the correct option for the figure shown below.

 

Q.40.

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 cu.m , then the rise in the water level in the tank will be:

Q.41.

Three solid cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find the surface area of the cube so formed

Q.42.

Find the curved surface area (in cm2) of a right circular cylinder of diameter 14 cm and height 8 cm.

 

Q.43.

A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

Q.44.

The height of the wall is 6 times its width and lenght of the wall is 7 times its height .if the volume of the wall be 16128 cu.m.its width is

Q.45.

Two cones have their heights in the ratio 1:3 and the radii of their bases in the ratio 3:Find the ratio of their volumes.

Q.46.

A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:

Q.47.

A rectangular block has the dimensions 5x6x7 cm it is dropped into a cylindrical vessel of radius 6cm and height 10 cm. If the level of the fluid in the cylinder rises by 4 cm, What portion of the block is immersed in the fluid ?

Q.48.

For the circle shown below, find the length (in cm) of the largest cord of the circle.

 

 

Q.49.

A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

Q.50.

If the area of three Adjacent faces of a cuboidal box are 120 cm², 72 cm², and 60 cm² respectively, then the volume of the box is