Question

A cylindrical tank is 1 m high and 0.3 m radius. If height is increased by 5 cm and radius by 1 cm what is the effect on volume?

Answer 1

Increase by 34264 cm³

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Use the formula for the volume of a cylinder:

• V = πr²h

Initially, the radius is 0.3 m = 30 cm and the height is 1 m = 100 cm.

Substituting these values into the formula, we get:

• V₁ = 3.142 × (30 cm)² × 100 cm = 282780 cm³

After increasing the height by 5 cm and the radius by 1 cm, the new height is 105 cm and the new radius is 31 cm. Substituting these values into the formula, we get:

• V₂ = 3.142 × (31 cm)² × 105 cm = 317044 cm³

The effect on volume can be calculated by finding the difference between V₂ and V₁:

• V₂ - V₁ = 317044 cm³ - 282780 cm³ = 34264 cm³

Therefore, increasing the height by 5 cm and the radius by 1 cm increases the volume of the cylindrical tank by 34264 cm³.