Question

a cylindrical jug of radius 8cm and height 10cm is filled with orange juice it is then poured into small conical cups of radius 2cm and height 6cm. find the number of cups that can be filled​

Answer 1

Given,

The radius of the cylindrical jug = 8cm

Height of the jug = 10 cm

Radius of the cup = 2 cm

Height of the cup = 6 cm

To Find,

The number of cups that can be filled

Solution,

The volume of the cylindrical jug = πr²h

                                          = π(8)(8)(10)

                                          = 640*π

The volume of the conical cup = 1/3πr²h

                                      = 1/3π(2)(2)(6)

                                      = 8π

Number of cups that can be filled = volume of cylinder/volume of cup

                                                         = 640π/8π

                                                         = 80

Hence, the number of cups that can be filled is 80.

Answer 2

The number of cups that can be filled​ is 80.

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Let's understand a few concepts:

To calculate the number of cups we will use the following formulas:

• $\boxed{\bold{Volume\: of\:cylinder = \pi r^2 h }}$

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

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Let's solve the given problem:

For Cylindrical Jug:

The radius of the cylindrical jug (r) = 8 cm

The height of the cylindrical jug (h) = 10 cm

∴ The volume of the cylindrical jug is,

= $\pi r^2h$

= $\frac{22}{7} \times 8^2\times 10$

= $\bold{2011.42 \:cm^3}$

For Small Conical Cup:

The radius of the conical cup (r) = 2 cm

The height of the conical cup (h) = 6 cm

∴ The volume of one small conical cup is,

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

= $\frac{1}{3} \times \frac{22}{7} \times 2^2\times 6$

= $\bold{25.14 \:cm^3}$

Therefore,

The number of conical cups that can be filled with the cylindrical jug is,

= $\frac{Volume\:of\:Cylinder}{Volume \:of\: 1\:small\:Cone}$

= $\frac{2011.42}{25.14}$

= $\bold{80}$

Thus, the number of conical cups that can be filled by the cylindrical jug  is 80.

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