Question

the volume of cylinder is 6776 cm² and its radius is 14 cm. find its lateral surface area and total surface area. ​

Answer 1

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

Answer 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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