Explanation
here we have a figure compounded by a sphere and a cylinder, so the total volume of the figure is teh sum of teh Sphere and cylinder areas, so
so
total volume= volume of the cylinder+volume of sphere+
replace
[tex]V_t=(\pi\cdot(r_{cyl})^2\cdot h)+\frac{4}{3}\pi(r_{sphe}^3)[/tex]
so, Let
[tex]\begin{gathered} \text{radius}_{cyl\in der}=\frac{diameter}{2}=\frac{10}{2}=5\text{ cm} \\ h=4\text{ cm} \\ \text{and} \\ \text{radius}_{sphere\text{ }}=3\text{ cm} \\ \pi=3 \end{gathered}[/tex]
now, replace in the expression
[tex]\begin{gathered} V_t=(3\cdot(5cm)^2\cdot4cm)+\frac{4}{3}(3)(3^3_{}cm^3) \\ V_t=3\cdot25cm^2\cdot4cm+4(27cm^3) \\ V_t=300cm^{^3}+108cm^3 \\ V_t=408cm^{^3} \end{gathered}[/tex]
therefore, the answer is
[tex]V_{}\approx408cm^{^3}[/tex]
I hope this helps you
