Question 1

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?

Accepted Answer

Volume required in the tank = (200 x 150 x 2) cu.m = 60000 cu.m Length of water column flown in1 min =(20 x 1000)/60 m =1000/3 m Volume flown per minute = 1.5 x 1.25 x (1000/3) cu.m= 625 cu.m. Required time = (60000/625)min = 96min

Question 2

A cylindrical rod of iron, whose height is equal to its radius, is melted and cast into spherical balls whose radius is half the radius of the rod. Find the number of balls.

Accepted Answer

Volume of rod = πr 2 h = πr 2 × r = πr 3 Volume of one spherical ball =r/2 Volume of the spherical ball = 4 3 πr 3 8 Number of balls=Volumeof rod/volumeof one ball

Question 3

A rectangular box measures internally 1.6m long, 1m broad and 60cm deep. The number of cubical box each of edge 20cm that can be packed inside the box is:

Accepted Answer

Number of blocks = 160 × 100 × 60 20 × 20 × 20 =120

Question 4

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

Accepted Answer

Let width = x Then, height = 6x and length = 42x 42x * 6x * x = 16128 x = 4

Question 5

Which measurement unit represents volume?

Accepted Answer

All of the above

Question 6

If the radius of base and height of a cone are increased by 10%, find the percentage of increase of its volume

Accepted Answer

v1= 1 3 πr 1 2 h 1 v2= 1 3 πr 2 2 h 2 % Increase in volume = (V2-V1) / (V2*100)

Question 7

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 ?

Accepted Answer

Volume of water flowing through 1 pipe of diameter x = Volume discharged by 6 pipes of diameter 12 cms. As speed is same, area of cross sections should be same. Area of bigger pipe of diameter x = Total area of 6 smaller pipes of diameter 12 i.e πR 2 = 6 πR 1 2 Here R = R and R1 = 12/2 = 6 ⇒ R 2 = 6 × 6 × 6 R = 14.696 => D = X = 14.696 * 2 = 29.3938 cm.

Question 8

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

Accepted Answer

4 × 3 . 14 × r 2 : 4 × 3 . 14 × r 2 = 1 : 2

Question 9

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.

Accepted Answer

Let l, b the sides of the base, so that the area of the base = lb remains constant. Let ‘h’ be the height of the solid. Volume of the solid, V = l× b× h. Since the volume is to be increased by 50%

Question 10

A store owner is packing books into larger boxes that measure 25 by 42 by 60 inches. If the measurement of each book is 7 by 6 by 5 inches, then how many books can be placed in the box ?

Accepted Answer

Number of books that can be placed in the larger box is given by Volume of Box / Volume of book. Now, n = 25 x 42 x 60 / 7 x 6 x 5 = 63000 / 210 = 300. Therefore, 300 books can be in that box.

Question 11

How many squares with sides 1/2 inch long are needed to cover a rectangle that is 4 ft long and 4 ft wide ?

Accepted Answer

It takes four of those little squares -- each one 1/2 inch on a side -- to cover one square inch. That's because each one is 1/2 x 1/2, or 1/4 of a square inch. In a rectangle that is 48 inches by 48 inches, there are 2304 square inches.(1 ft = 12 inches) Since it takes 4 little squares to cover 1 sq inch, then it would need 2304 x 4 squares (1/2 inch on a side each) to cover a rectangle 4 feet by 4 feet. That is 9,216 of those squares.

Question 12

88 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be ?

Accepted Answer

Vol of silver = πR 2 h = 66 C.C Given D= 1mm => R = D/2 = 1/20 cm => 22 7 × 1 20 2 × h = 66 = 66 x 400 x (7/22) = 8400 cm = 84 mtrs.

Question 13

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 ?

Accepted Answer

Since level of water increased in cylinder by height 4. This is because of the rectangular block . Therefore , area of rectangular block immersed in water is = 22 7 × 6 × 6 × 4 Thats why portion of block immersed in water is = (22/7 * 36 * 4) / total vol. of rectangle = (22/7 * 36 * 4)/ (7*5*6) = (22/7 * 24)/ 35.

Question 14

66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

Accepted Answer

Let the length of the wire be h. Radius r =1/2 mm = 1/20 cm πr 2 h = 66 => h= (66 x 20 x 20) x (7/22) = 8400cm = 84m

Question 15

What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?

Accepted Answer

h = 14 cm, r = 7 cm. So, l = 7 2 + 14 2 = 245 = 7 5 c m Total surface area = πrl + πr 2 = 22 7 × 7 × 7 5 + 22 7 × 7 × 7 = 154 5 + 1 = (3.236 x 154) sq.cm = 498.35 sq.cm

Question 16

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

Accepted Answer

We know that, One square meter is equal to 10,00,000 sq mm. Given, each mesh is 8mm length and 5mm wide Therefore for each mesh : 8 x 5 = 40 sq mm. So, number of meshes = 1000000 40 = 25000.

Question 17

Solve the triangle b=36 a=38 c=18 for perimeter of the triangle?

Accepted Answer

92 units

Question 18

The diagonal of the floor of a rectangular closet is 712 feet. The shorter side of the closet is 412 feet. What is the area of the closet in square feet?

Accepted Answer

Other side= 15 2 2 - 9 2 2 f t = 225 4 - 81 4 f t = 144 4 = 6ft Area of closet =(6 x 4.5)sq.ft = 27 sq.ft

Question 19

Calculate the number of bricks, each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 m x 5 m when 10% of its volume is occupied by concrete ?

Accepted Answer

Let 'B' be the nuber of bricks. => 10 x 4/100 x 5 x 90/100 = 25/100 x 15/100 x 8/100 x B => 10 x 20 x 90 = 15 x 2 x B => B = 6000

Question 20

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

Accepted Answer

720 cub.cm

Volume and Surface Area Questions