Question

two solids of right shape are 49 cm and 35 cm high and their base diameters are 16 cm 40 cm respectively both are melted and moulded into a single cylinder is 56 cm find its base diameter

Answer 1

Solution :-

Let r1 and r2 be the respective radii of first and second cylinder.

Diameter of 1st cylinder = 16 cm 
Radius = r1 = 16/2 = 8 cm

Diameter of 2nd cylinder = 14 cm
Radius = r2 = 14/2 = 7 cm

Height of 1st cylinder = h1 = 49 cm
Height of 2nd cylinder = h2 = 35 cm

Volume of 1st cylinder = πr1²h

⇒ (22*8*8*49)/7

⇒ 9856 cm³

Volume of 2nd cylinder = πr2²h

⇒ (22*7*7*35)/7

⇒ 5390 cm³

Total volume = 9856 cm³ + 5390 cm³ = 15246 cm³

Let radius of new cylinder be r.

⇒ Volume of 1st and 2nd cylinder = Volume of the new cylinder

⇒ 15246 cm³ = (22*r²*56)/7

⇒ r² = 106722/1232

⇒ r² = 86.625 cm

⇒ r = √86.625

⇒ r = 9.307 cm

⇒ diameter = 9.307*2 = 18.614 cm

So, the diameter of the new cylinder is 18.614 cm

Answer.