Question

Water flows, at 9 km per hour, through a cylindrical pipe of cross-sectional area 25 cm2. If this water is collected into a rectangular cistern of imensions 7.5 m by 5 m by 4 m; calculate therise in level in the cistern in 1 hour 15 minutes. 

 

Calculate:
(a) the total surface area,
(b) the total volume of the solid and
(c) the density of the material if its total weight is 1.7 kg.. 

Answer 1

 

Diameter = 10 cm
Therefore, radius (r) = 5 cm
Height of the cone (h) = 12 cm
Height of the cylinder = 12 cm 

`∴ l=sqrt(h^2+r^2)=sqrt(12^2+5^2)=sqrt(144+25)=sqrt169=13 cm ` 

(1) Total surface area of the solid 

=`pirl+2pirh+2pir^2` 

=`pir(l+2h+2r) ` 

=`22/7xx5[13+2(12)+(2xx5)]` 

=`110/7[13+24+10]` 

=`110/7xx47`  

=`5170/7`     

=`738.57 cm^2`      

(2) Total volume of the solid 

`=1/3pir^2h+2/3pir^3` 

`=pir^2[1/3h+h+2/3r]` 

`=22/7xx5xx5[1/3xx12+12+2/3xx5]`  

`=550/7[4+12+10/3]`  

`=550/7[16+10/3]` 

`=55/7xx58/3`  

`=31900/21` 

=` 1519.0476cm^3` 

(3) Total weight of the solid=1.7kg 

`∴ Density=1.7xx1000/1519.0476" gm/cm 3"=1.119 "gm/cm"^3` 

⇒ Density =`" 1.12 gm /cm^3"`