Câu hỏi 8

Ta có: \(V\left( t \right) = \int {V'\left( t \right)dt}  = \int {\left( {a{t^2} + bt} \right)dt}  = \frac{{a{t^3}}}{3} + \frac{{b{t^2}}}{2} + C.\) 

Theo đề bài ta có: \(\left\{ \begin{array}{l}V\left( 0 \right) = 0\\V\left( 5 \right) = 15\\V\left( {10} \right) = 110\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}C = 0\\\frac{{125a}}{3} + \frac{{25b}}{2} = 15\\\frac{{1000a}}{3} + \frac{{100b}}{2} = 110\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}a = \frac{3}{{10}}\\b = \frac{1}{5}\end{array} \right.\)

\( \Rightarrow V\left( t \right) = \dfrac{1}{{10}}{t^3} + \dfrac{1}{10}{t^2} \Rightarrow V\left( {20} \right) = 840\,{m^3}.\)

Chọn  C.