Đáp án:
$\begin{array}{l}
1)\\
- cho:x = 0 \Rightarrow y = \dfrac{{\sqrt 2 }}{2} \Rightarrow B\left( {0;\dfrac{{\sqrt 2 }}{2}} \right)\\
- cho:y = 0 \Rightarrow x = \dfrac{{\sqrt 2 }}{2} \Rightarrow A\left( {\dfrac{{\sqrt 2 }}{2};0} \right)\\
\Rightarrow H\left( {\dfrac{{\sqrt 2 }}{4};\dfrac{{\sqrt 2 }}{4}} \right)\\
\Rightarrow OH = \sqrt {{{\left( {\dfrac{{\sqrt 2 }}{4}} \right)}^2} + {{\left( {\dfrac{{\sqrt 2 }}{4}} \right)}^2}} = \dfrac{1}{2} = 0,5\left( {cm} \right)\\
2)\\
h = 12cm;r = 2cm\\
\Rightarrow {V_{coc}} = \pi .{r^2}.h = 48\pi \left( {c{m^3}} \right)\\
{h_{nuoc}} = 8cm\\
\Rightarrow {V_{nuoc}} = \pi .{r^2}.8 = 32\pi \left( {c{m^3}} \right)\\
{R_{bi}} = 1cm\\
\Rightarrow {V_{bi}} = 6.\left( {\dfrac{4}{3}.\pi .{R^3}} \right) = 12\pi \left( {c{m^3}} \right)\\
\Rightarrow {V_{nuoc}} + {V_{bi}} = 44\pi \left( {c{m^3}} \right)\\
\Rightarrow h' = \dfrac{{44\pi }}{{\pi .{r^2}}} = \dfrac{{44\pi }}{{\pi {{.2}^2}}} = 11\left( {cm} \right)
\end{array}$
=> mực nước cách miệng cốc 12-11=1 (cm)
Vậy mực nước cách miệng cốc 1cm
