Question

A candle maker has rectangular block of paraffin that is 4 centimeter high by 8 centimeter long by 6 centimeter wide. He melts it into a cone-shaped candle that is 5 centimeter wide at the base and 25 centimeter tall. Does the candle use all the paraffin from the original block?justify your reasoning

Answer 1

The candle will not use all the paraffin from the original block.

Explanation:

The cone-shaped candle is 5 cm wide at the base i.e. the diameter of the base is 5 cm i.e. radius is 2.5 cm.

If the height of the cone is 25 cm, then total volume of the cone shaped candle is

`(1)/(3)\pi  r^(2) h`

=
`(22 * 2.5^(2) * 25 )/(3 * 7)`

= 163.69 cubic cm.

Again, the volumes of the rectangular block of paraffin is (4 × 8 × 6) = 192 cubic cm.

Since, 192 > 163.69

Therefore, the candle will not use all the paraffin from the original block.