the volume of cylinder is 6776 cm² and its radius is 14 cm. find its lateral surface area and total surface area.
Answers
Answer:
volume of cylinder is 6776cm^2
radius is 14cm
volume is πr^2h
22/7×14×14×h=6776
22×2×14×h=6776
616×h=6776
h=6776/616
h=11
lateral surface area=2πrh
2×22/7×14×11
2×22×2×11
768cm^2
total surface area=2πr(r+h)
2×22/7×14(14+11)
2×22×2×124
10956cm^2
Given:-
- Volume of cylinder = 6776 cm²
- Radius of its base = 14 cm
To Find:-
- Lateral Surface Area of the cylinder
- Total Surface Area of the cylinder
Solution:-
We are given with the Volume and radius of base of the cylinder through which we'll find the height of the cylinder.
We know,
✭ Volume of cylinder = πr²h
Hence,
6776 = πr²h
=> 6776 = 22/7 × (14)² × h
=> 6776 = 22/7 × 14 × 14 × h
=> 6776 = 22 × 2 × 14 × h
=> 6776 = 616h
=> h = 6776/616
=> h = 11 cm
Therefore the height of the cylinder is 11 cm
Now,
We know,
✭ TSA of a cylinder = 2πr(r + h) sq.units
Hence,
TSA = 2 × 22/7 × 14 (14 + 11)
=> TSA = 2 × 22 × 2 × 25
=> TSA = 88 × 25
=> TSA = 2200 cm²
Therefore the TSA of the cylinder is 2200 cm²
Now,
We also know,
✭ LSA of cylinder = 2πrh
Hence,
LSA of cylinder = 2 × 22/7 × 14 × 11
=> LSA = 2 × 22 × 2 × 11
=> LSA = 88 × 11
=> LSA = 968 cm²
Therefore the LSA of the cylinder is 968 cm².
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