Step-by-step explanation:
Now, Given that:-
Diameter (d) = 10 cm
So, Radius (r) = 10/2 = 5cm
Height of the cylinder = 12cm.
[tex]volume \: of \: the \: cylinder \: = \pi {r}^{2} h[/tex]
[tex] = > \pi \times {5}^{2} \times 12 {cm}^{3} = 300\pi {cm}^{3} [/tex]
Radius of the cone = 5 cm.
Height of the cone = 12 cm.
[tex]slant \: height \: of \: the \: cone \: = \sqrt{ {h}^{2} + \: {r}^{2} } [/tex]
[tex] = > \sqrt{ {5}^{2}+{12}^{2} } cm \: = 13cm[/tex]
Volume of the cone = 1/3 *πr^2h
[tex] = > \frac{1}{3} \pi \times {5}^{2} \times 12 {cm}^{3} = 100\pi {cm}^{3} [/tex]
therefore, the volume of the remaining solid
[tex] = 300\pi {cm}^{3} - 100\pi {cm}^{3} \\ = 200 \times 3.14 {cm}^{3} = 628 {cm}^{3} [/tex]
Curved surface of the cylinder =
[tex]2\pi \: rh \: = 2\pi \times 5 \times 12 {cm}^{2} \\ = 120\pi {cm}^{2} .[/tex]
[tex]curved \: surface \: of \: the \: cone \: = \pi \: rl \\ = \pi \times 5 \times 13 {cm}^{2} \\ = 65\pi {cm }^{2} \\ area \: of \: (upper)circular \: base \: \\ of \: cylinder \: = \\ = \pi \: {r}^{2} = \pi \times {5}^{2} [/tex]
therefore, The whole surface area of the remaining solid
= curved surface area of cylinder + curved surface area of cone + area of (upper) circular base of cylinder
[tex] = 120\pi {cm}^{2} + 65\pi {cm }^{2} + 25 \pi {cm}^{2} \\ = 210 \times 3.14 {cm}^{2} = 659.4 {cm}^{2} [/tex]
