Question

the total surface area of a cylinder is 6512 cm square and the circumference of its base is 88 cm. Find its radius and its volume??

Answer 1

Here the circumference base means the circumference of circle,

2πr = 88

2×22/7×r = 88

44/7×r = 88

r = 88×7/44

r = 14

Hence, the radius of the cylinder is 14 cm

Now, we have total surface area , radius , we need volume , and to find volume we need height , so let's find out height.

2πr(r+h) = 6512

2×22/7×14(14+h)=6512  

616/7 (14+h)=6512  

14+h=(6512×7)/616

h=74-14

h=60

Hence, the height of the cylinder is 60 cm

Now, let's find out volume.

πr²h = 22/7×14×14×60

Volume = 22×2×14×60

Volume = 36960

Hence, the volume of the cylinder is 36960 cm³

Answer 2

Answer :-

• Radius = 14cm
• Volume = 36960 cm³

Explanation :-

★Given :

• The total surface area of a cylinder is 6512 cm²
• Circumference of its base is 88 cm.

★To find :

• Radius
• Volume

★Solution :

Let r be the radius and h be the height of the given cylinder.

We know,

✦Circumference = 2πr

Given that circumference is 88cm.Therefore,

→2πr = 88 cm (Given)

→2 × 22/7 × r = 88 cm

→r = 88 × 7/22 × 1/2

→r = 14 cm

We also know :

✦Total surface area = 2πr(h + r)  

Therefore,

→2πr(h + r)  = 6512 cm²

→88(h + 14) = 6512   [As 2πr = 88]

→h + 14 = 6512/88

→h + 14 = 74

→h = 60 cm

Using the formula,

✦Volume of the cylinder = πr²h

Substituting the values,

→Volume = πr²h

→22/7 × (14)² × 60

→36960 cm³

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