Volume Solution3





In this page volume solution3 we are going to see solution of each questions of the worksheet volume worksheet1.

Question 7:

A rectangular sheet of metal foil with dimension 66 cm x 12 cm is rolled to form a cylinder of height 12 cm. Find the volume of the cylinder.

Solution:

Length of metal sheet = 66 cm

Width of sheet = 12 cm

Now the metal sheet is in the form of cylinder. Here height of the cylinder is also 12 cm. Now 66 cm is to be considered as circumference of the base of the cylinder.

circumference of the base of the cylinder = 66 cm

                                                   2 Π r = 66

                                       2 x (22/7) x r = 66

                                                       r = 66 x (1/2) x (7/22) 

                                                       r = 3 x (1/2) x (7)

                                                       r = 21/2

                                                       r = 10.5 cm


Volume of the right circular cylinder =  Π r² h

                                                   = (22/7) x (10.5)² x 12

                                                   = (22/7) x (10.5) x(10.5) x 12

                                                   = (22) x (1.5) x (10.5) x 12

                                                   = 4158 cm³

Volume of the the right circular cylinder = 4158 cm³


Question 8:

A lead pencil is in the shape of right circular cylinder. The pencil is 28 cm long and its radius is 3 mm. If the lead is of radius 1 mm,then find the volume of the wood used in the pencil.

Solution:

Height of the pencil = 28 cm

Outer radius (R) = 3 mm

Inner radius (r) = 1 mm

Now we have to change the units from mm to cm. For that we have to divide it by 10.

             R = 3/10 = 0.3 cm

             r = 1/10 = 0.1 cm

To find the volume of the wood used to make that pencil,simply we can find the volume of the pencil.Pencil is in the shape of hollow cylinder

           Volume of hollow cylinder = Π h (R² - r²)

                                                = (22/7) x 28 x (0.3² - 0.1²)

                                                = (22) x 4 x (0.09 - 0.01)

                                                = (22) x 4 x (0.08)

                                                = 7.04 cm³

Volume of wood used in the pencil = 7.04 cm³

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