Question

two solids of right cylindrical shape are 49 cm and 35 cm high and their base diameter are 16 cm and 14 cm respectively. Both are melted and moulded into a single cylinder, 56 cm high. 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.

Answer 2

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 18.6 cm