two solution right cylinder cassette part 49 cm and 35 cm high and their base diameter are 16 cm 14 cm respectively both are melted and moulded into a single cylinder 56 cm find its diameter
Answers
Answer:
Step-by-step explanation:
∴ Let , r1 and r2 be the respective radii of first and second cylinder.
∴ Diameter of 1st cylinder = 16 cm ......... given
Radius = r1 = 16/2 = 8 cm
∴ Diameter of 2nd cylinder = 14 cm
= 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
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Hey there
Here ur answer
Given:
Height of 1st cylinder = 49 cm
Height of 2nd cylinder = 35 cm
Base diameter of 1st cylinder = 16 cm
Base diameter of 2nd cylinder = 14 cm
Single cylinder = 56 cm
Solution:
Let x1 and x2 be the 1st and 2nd cylinder.
Thn,
Diameter of 1st cylinder:
So,
Radius = x1
= 16/2
= 8 cm
Diameter of 2nd cylinder:
Thn,
Radius= x2
= 14/2
= 7 cm
Thn,
Height of 1st cylinder = 49 cm
Height of 2nd cylinder = 35 cm
Volume of cylinder = πr²h
To find volume of 1st cylinder:
→ (22×8×8×49)/7
→ 9856 cm³
To find volume of 2nd cylinder:
→ (22×7×7×35)/7
→ 5390 cm³
For finding total volume:
Total volume = 1st volume + 2nd volume
= 9856 cm³ + 5390 cm³
= 15246 cm³
Let radius of new cylinder be y.
→ Volume of 1st and 2nd cylinder = Volume of the new cylinder
→15246 cm³ = (22*r²*56)/7
→ y² = 106722/1232
→ y² = 86.625 cm
⇒ y = √86.625
⇒ y = 9.307 cm
⇒ Diameter = 9.307*2
= 18.614 cm
∴ So, the diameter of the new cylinder is 18.614 cm
Hope this helps u
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