CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

A metallic bucket,open at the top, of height 24 cm is in the from of the frustum of a cone, the radii of whose lower and upper circular ends are 7 cm and,respectively.Find (i) the volume of water which can completely fill the bucket;
 (ii) the care of the metal sheet used to make the bucket.


Solution

Radius of lower circular end $$= r = 7 cm$$
 Radius of upper circular end $$= R = 14 cm$$
 height of bucket $$= h = 24 cm$$

 Slant height of frustum:

$$ l =  \sqrt { \left( R-r \right) ^ 2+h^ 2 }  $$

$$ =\sqrt { \left( 14-7 \right) ^ 2+24^ 2 }  $$

$$ =\sqrt {7^2+24^2} $$

$$= \sqrt{625} $$

 $$= 25 cm$$

 (i) Volume of frustum of cone $$ = \dfrac{1}{3} \pi h (R^2 + r^2 + Rr)cm^3 $$

 $$ = \dfrac{1}{3} \times \dfrac{22}{7} \times 24 (14^2 + 7^2 + 14 \times 7) $$

 $$ =\dfrac{1}{3} \times \dfrac{22}{7} \times 24 \times (196 + 98+49) $$

 $$ =\dfrac{1}{3} \times \dfrac{22}{7} \times 24 \times (343) $$

 $$= 8624 cm^3$$ 

 (ii) Curved surface area $$= x (R+r)$$

$$=22/7 \times 25 \times (14 + 7)$$

 $$= 1650 cm^2$$

 Area of the base of bucket = $$ \pi  r^2$$ 

 (consider the lower base of a bucket)

 $$= 22/7 \times 7 \times 7$$

 $$= 154 cm^2$$

 Area of metal sheet used to make the bucket = curved surface area + Area of the base 
$$ = 1650 + 154$$ 
 $$= 1804 $$
 Area pf metal sheet used to make the bucket is $$1804 cm^2$$

Mathematics
RS Agarwal
Standard X

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
Same exercise questions
View More


similar_icon
People also searched for
View More



footer-image