Question

The volume V, in cubic centimeters, of 1 kilogram of water at a temperature T (in Celsius) is given approximately by the formula V ( T ) = − 6.8 × 10 − 5 T 3 + 8.5 × 10 − 3 T 2 − 6.4 × 10 − 2 T + 9.99 × 10 2 where 0 C ≤ T ≤ 30 C. Find the temperature at which water has its minimum volume. Round your final answer to 2 decimal places.

Answer 1

Answer: V = 9990 cubic centimeter

Explanation:

Given that the volume V in cubic centimeters, at a temperature T (in Celsius) is given approximately by the formula

V ( T ) = − 6.8 × 10 ^− 5 T 3 + 8.5 × 10 − ^3 T 2 − 6.4 × 10 − ^2 T + 9.99 × 10^2 where 0 C ≤ T ≤ 30 C.

Water has its minimum volume at low temperature. That is T = 0

Therefore,

V(0) = - 6.8 × 10 − 5 (0) 3 + 8.5 × 10 − 3 (0) 2 − 6.4 × 10 − 2 (0) + 9.99 × 10^2

V(0) = 99.9 × 100

V(0) = 9990 cubic centimeter