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A conical flask is full of water. The flask has base radius r and height h, This water is poured into a cylindrical flask of base radius mr. The height of water in the cylindrical flask is ?

A.

h/2

B.

2h/m

C.

h/3m^{2}

D.

m/2h

Answer with explanation

Answer: Option CExplanation

Volume of water = Volume of conical flask = (1/3)πr^{2}h

Now, the water is poured into cylindrical flask.

∴ Volume of cylinder = Volumes of water

⇒ π (mr)^{2} x Height = (1/3)πr^{2}h

∴ Height = h/3m^{2}

Workspace

How many metal balls each of radius 2 cm can be made by melting a big metal ball whose radius is 8cm.

A.

729

B.

81

C.

78

D.

64

Answer with explanation

Answer: Option DExplanation

Radius of larger ball = 8 cm

So ,

Volume of larger ball = 4/3 * pie * ( 8) ³ cm³

And ,

Radius of smaller ball = 2 cm

Volume of smaller ball = 4/3 * pie * ( 2 ) ³ cm³ .

Let the number of mmaller balls be x .

A / q ,

x * 4/3 * pie * ( 2 ) ³ = 4/3 * pie * ( 8 ) ³

=> x = 4 * 4 * 4

=> x = 64 .

Required number of balls = 64 .

Workspace

The diameter of two cones are equal. If their slant height are in the ratio 7:4 . Then the ratio of their curved surface areas are

A.

15:11

B.

2:1

C.

3:5

D.

7 : 4

Answer with explanation

Answer: Option DExplanation

Since the diameters of two cones are equal, their radius will also be the same.

Let the slant height of the two cones be l₁ and l₂ respectively.

Therefore,

l₁ : l₂ = 7 : 4

The curved surface area of the two cones are

πrl₁ and πrl₂

So, the ratio of their curved surface area are

πrl₁/πrl₂

π and r are cancelled.

⇒ l₁/l₂ = 7/4

So, the ratio of the curved surface area of two cones is 7 : 4

Answer.

Workspace

The volume of a cube is 4096cm3 then its surface area is

A.

1536 sq.cm

B.

1164 sq.cm

C.

2212 sq.cm

D.

188 sq.cm

Answer with explanation

Answer: Option AExplanation

Volume =4096 cm cube

Volume =side 3

Side=cube root of 4096

Side = 16cm

Therefore surface area =6×side 2=6×16^2

============6×256

============1,536cm

Workspace

Find the side of a cube whose surface area is 2400cm square.

A.

4800 cu.cm

B.

8000 cu.cm

C.

400 cu.cm.

D.

20 cm

Answer with explanation

Answer: Option DExplanation

Since the cube has 6 faces divide it by 6.

= 2400 ÷ 6

=400

1 face = 400 area

since the surface of the cube is square and its area is ‘side square’

find the square root of 400

which is 20 cm (side)

Workspace

If the number of square centimeters in the surface area of a sphere is equal to the number of cubic cm in its volume. find the diameter cf the sphere

A.

6

B.

3

C.

8

D.

4

Answer with explanation

Answer: Option AExplanation

The clue given can be put in an equation and solved for the radius. The diameter is then d=2r. 4πr3/3 = 4πr2 r3 – 3r2 = 0 r2(r-3) = 0 Since r>0, we conclude that r=3 cm. Thus the diameter is 6 cm.

Workspace

A hollow cylindrical tube open at both ends is made of iron 3 cm thick. if the external diameter be 56 cm n the length of the tube be 182 cm, find the number of cubic cm in it.

A.

90865.32cm³

B.

85000 cu.cm

C.

48000 cu.cm

D.

34678 cu.cm

Answer with explanation

Answer: Option AExplanation

Given, thickness of iron =3cm

external diameter = 56cm

Length of tube = 182cm

We know,

volume of hollow cylinder = πh(R²−r²)

∴ internal diameter = external diameter−2×thickness of iron

= 56−2×3

= 56−6

= 50cm

=> Outer radius(R) = 56÷2 = 28cm

inner radius(r) = 50÷2 = 25cm

∴ Volume of hollow cylinder = πh(R²−r²)

= 3.14×182(28²−25²)

= 3.14×82×159

= 90865.32cm³

Workspace

How many cm of paper sheet 10cm wide will be required to make a cone, the radius of whose base is 9 cm and whose height is 12cm.

A.

45.50

B.

24

C.

42.28

D.

29

Answer with explanation

Answer: Option CExplanation

slant height = sqrt (12^2+9^2) = 15

Tota perimeter of the cone = 2*22/7*9+15+15+18 = 56.57+48=104.57

paper perimeter = 2(L+10)= 104.57

L=52.28-10 = 42.28

Workspace

A.

90865.32

B.

8500 cu.cm

C.

4800 cu.cm

D.

3467.80 cu.cm

Answer with explanation

Answer: Option AExplanation

Given, thickness of iron =3cm

external diameter = 56cm

Length of tube = 182cm

We know,

volume of hollow cylinder = πh(R²−r²)

∴ internal diameter = external diameter−2×thickness of iron

= 56−2×3

= 56−6

= 50cm

=> Outer radius(R) = 56÷2 = 28cm

inner radius(r) = 50÷2 = 25cm

∴ Volume of hollow cylinder = πh(R²−r²)

= 3.14×182(28²−25²)

= 3.14×82×159

= 90865.32cm³

Workspace

The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3.

Calculate the ratio of their volumes and the ratio of their curved surfaces.

A.

10/9

B.

18/10

C.

21/25

D.

8/3

Answer with explanation

Answer: Option AExplanation

Let the radii be 2x and 3x

let the height be 5y and 3y

so,

ratio of volume =r²h/R²H =(2x)²×5y/(3x)²×3y =20x²y/27x²y =20/27

ratio of CSA =rh/RH =2x×5y/3x×3y =10xy/9xy =10/9

Workspace

The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3.

Calculate the ratio of their volumes and the ratio of their curved surfaces.

A.

80

B.

40

C.

10/9

D.

1600

Answer with explanation

Answer: Option CExplanation

Let the radii be 2x and 3x

let the height be 5y and 3y

so,

ratio of volume =r²h/R²H =(2x)²×5y/(3x)²×3y =20x²y/27x²y =20/27

ratio of CSA =rh/RH =2x×5y/3x×3y =10xy/9xy =10/9

Workspace

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?

A.

2 : 1

B.

3 : 2

C.

25 : 18

D.

27 : 20

Answer with explanation

Answer: Option CExplanation

Workspace

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box

A.

4830

B.

5120

C.

6420

D.

8960

Answer with explanation

Answer: Option BExplanation

Clearly, *l* = (48 – 16)m = 32 m,

*b* = (36 -16)m = 20 m,

*h* = 8 m.

Volume of the box = (32 x 20 x 8) m^{3} = 5120 m^{3}.

Workspace

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

A.

75 cubic meter

B.

750 cubic meter

C.

7500 cubic meter

D.

75000 cubic meter

Answer with explanation

Answer: Option BExplanation

1 hectare = 10,000 m^2

Area = (1.5 x 10000) m^2 = 15000 m^2.

Depth = 5/100 m=1/20 m

Volume = (Area x Depth)

=15000 x1/20 m^3

= 750 m^3

Workspace

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