Question

two cylindrical vessels are filled with water the radius of vessels is 15 cm and its height is 25 cms the radius and he got of other vessels are 10 cm and 18cm respectively find the radius of cylindrical vessels of height 30 cm which will just contain the water of the 2 given vessels

Answer 1

RADIUS of 1st cylinder(R)=15             RADIUS of 2 nd cylinder(r)=10
HEIGHT  of 1st cylinder(H)=25           HEIGHT  of 2nd cylinder(h)=18
Height of the biggest cylinder(H-1)=30  radious of the biggest cylinder(R-1)=?
volume of cylin...= 22/7*r*r*h
volume of:-
             1 st cylin...+2 nd cylin...=3 rd cylin....
                  (22/7*15*15*25) + (22/7*10*10*18)= (22/7*(R-1)*(R-1)*30)
                        =>taking the common outside,
                  22/7*5*5*(3*3*25+2*2*18) = 22/7*(R-1)*(R-1)*30
                        => 22/7 appears on both RHS and LHS, and will get canacelled!
   so,           25*(225+72) = (R-1)*(R-1)*30
                  25(297) = (R-1)*(R-1)*30
                  7425 = (R-1)*(R-1)*30
                  7425/30 = (R-1)*(R-1)
                  247.5 =  (R-1)*(R-1)
                        =>root of ( 247.5), i.e. 15.7=  (R-1)

Answer 2

$\huge \underline \mathbb {SOLUTION:-}$

Given:

• Radius of 1st cylinder = 15cm
• Height of 1st cylinder = 40 cm

• Radius of 2nd cylinder = 20 cm
• Height of 2nd cylinder = 45 cm

• Also, height of new cylinder = 30 cm

ExPlanation:

Let the radius of new cylinder be r cm.

Sum of volumes of 1st and 2nd cylinder = volume of new cylinder

π × 152× 40 + π × 202× 45 = πr²× 30

⇒(225 × 40 + 400 × 45) = r² × 30

⇒ 9000 + 18000 = r² × 30

⇒ 27000 = r² × 30

⇒ r² = 900

⇒ r² = 302

⇒ r = 30 cm

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