Volume Solution6





In this page volume solution6 we are going to see solution of each questions of the worksheet volume worksheet1.

Question 13:

A right angled triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the fixed side of 12 cm. Find the volume of the solid generated.

Solution:

In any right triangle the longer side must be hypotenuse side. The longer side of the given sides is 13 cm. So it must be hypotenuse side of the triangle.

From the diagram we know that slant height is 13 cm, radius is 5 cm and height is 12 cm.

L = 13 cm

r = 5 cm

h = 12 cm

Volume of cone = (1/3) Πh

                       = (1/3) x (22/7) x (5²) x (12)

                       = (22/7) x (5) x (5) x (4)

                       = (88/7) x (25) 

                       = (2200/7)

                       = 314.29 cm³

Volume of cone = 314.29 cm³


Question 14:

The radius and height of a right circular cone are in the ratio 2:3. Find the slant height if its volume is 100.48 cu.cm (take Π = 3.14)

Solution:

Radius and height of right circular cone are in the ratio 2 : 3

                                    r : h = 2 : 3

                                    r/h = 2/3

                                       r = 2h/3

Volume of cone = 100.48 cu.cm

     (1/3) Πh  = 100.48

     (1/3) (3.14) (2h/3)² h  = 100.48

     (1/3) (3.14) (4h²/9) h  = 100.48

                                  h³ = 100.48 x (3/1) x (1/3.14) x (9/4)

                                  h³ = 32 x (3/1) x (9/4)

                                  h³ = 8 x 27

                                  h = 2 x 2 x 2 x 3 x 3 x 3

                                 h = 2 x 3

                                  h = 6 cm

                                  r = 2 (6)/3

                                  r = 2 x 2

                                  r = 4 cm 

                 L²r² + h²

                      = 4² + 6²

                      = 16 + 36

                      = √ 52

                 L = 2 √13 cm

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