10th Maths Surface Areas and Volumes The Schoolhouse

MATHEMATICS Ex.21 A bucket of height 16 cm and made up of metal metal sheet is in the form of frustum of a right circular cone with with radii of its lower and upper ends as 3 cm and 15 cm respectively. Calculate: (i) the height of the cone of which the bucket is a part. (ii) the volume of water which can be filled in the bucket. (iii) the slant height of the bucket. (iv) the area of the metal sheet required to make the bucket. Sol.

Let ABCD be the the bucket which is is frustum frustum of a cone with vertex vertex 0 (as shown shown in figure). Let ON = x cm

OAB  OMC 

 

 x

16  x  x

16  x

 

 ON   NB     OM   MC  

3 15 1 5



5 x  16  x1



x=4



4 x  16



ON = 4 cm and OM = 4 + 16 = 20 cm



the height of the cone = 20 cm volume of the bucket



1

(15) 2  20 

  

3

1 3

(3) 2  4cm 3

  

{i.e., Volume of the large cone – Volume of the small cone}



1 3

[225  20  36] cm 3

  

   [75  20  12] cm 3  1488   cm 3 Slant height of cone of radius 15 cm

 (15) 2  (20) 2 cm  625 cm  25 cm Slant height of cone of radius 3 cm

 

 (4) 2  (3) 2 cm  5 cm Slant height of bucket = ( 25  5) cm  20 cm, i.e,   20 cm 2 The area of the metal sheet     ( R  r )     r       20  (15  3)    (3) 2 cm 2  360    9   cm 2  369    cm 2

 Note. The area of the metal sheet used = C.S. of larger larger cone – C.S. of smaller cone + Area of the base of the bucket bucket

 [    25 15      5  3      (3) 2 ] cm 2  [375    15    9  ] cm 2  369    cm 2