Volume Solution5





In this page volume solution5 we are going to see solution of each questions of the worksheet volume worksheet2.

Question 11:

A vessel is in the form of frustum of a cone. Its radius at one end and the height are 8 cm and 14 cm respectively. If its volume is 5676/3 cm³,then find the radius at the other end.

Solution:

Volume of the frustum cone = (5676/3) cm³

Let "r" be the required radius

Radius (R) = 8 cm

height (h) = 14 cm

(1/3) Π h (R²+ r² + R r) = (5676/3)                  

(1/3) x (22/7) x (14) (8²+ r² + 8 r) = (5676/3)                  

(8²+ r² + 8 r) = (5676/3)x (3/1) x (7/22) x (1/14)                  

(64 + r² + 8 r) = (258)(7) x (1/14)                  

(64 + r² + 8 r) = (258)x (1/2)                  

r² + 8 r + 64 = 129

r² + 8 r + 64 -129 = 0

r² + 8 r - 65 = 0

(r + 13) (r - 5) = 0

 r + 13 = 0              r - 5 = 0

 r = -13                       r = 5 cm

Therefore required radius = 5 cm


Question 12:

The perimeter of the ends of a frustum of a cone are 44 cm and 8.4 Π cm. If the depth is 14 cm, then find its volume.

Solution:

Perimeter of upper end = 44 cm

Perimeter of lower end = 8.4 Π cm

Height of frustum cone =14 cm

Now we have to find the volume of frustum cone

Volume of the frustum cone = (1/3) Π h (R²+ r² + R r)

                         2 Π R = 44 

             2 x (22/7) x R = 44      

                             R = 44 x (1/2) x (7/22)

                             R = 2 x (1/2) x (7)

                             R = 7

                         2 Π r = 8.4 Π

                     2 x Π x r = 8.4 Π      

                             r = 8.4 Π x (1/2Π)

                             r = 4.2 

Volume of the frustum cone = (1/3) x (22/7) x (14) (7²+ 4.2² + 7(4.2))

                                        = (44/3) (49+ 29.4 + 17.64)

                                        = (44/3) (96.04)

                                        = (44) (32.013)

                                        = 1408.57 cm³

Volume of the frustum cone =  1408.57 cm³

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