Question

Find the volume of a cone if its total surface area is 7128 sq.cm and radius of base is 28cm.(pie=22÷7)

Answer 1

Answer:

TSA = πrl + πr² = 7128 cm²

πr² = ( 22/7 ) × 28 × 28 = 17248 / 7 = 2464 cm²

Now, 7128 = ( 22/7 ) × 28 × l + 2464

7128 - 2464 = ( 616 / 7 ) l

4664 = 88 l

l = 53 cm

It's slant height = 53cm = l

We need to find h, in order to find its volume

By using Pythagoras theorem,

Slant height ² = Height of cone ² + Radius ²

l ² = h ² + r ²

53 ² = h ² + 28 ²

2809 = h ² + 784

2809 - 784 = h ²

2025 = h ²

h = 45

Volume of cone = V = πr²h/3 = ( 22/7 ) × 28 × 28 × ( 45/3 ) = 258720 / 7 = 36960 cm³

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