<h3>Volume of the remaining solid = 628 cm^2</h3>
<h3>Whole surface area = 659.4 cm^2</h3>
Step-by-step explanation:
Now, Given that:-
Diameter (d) = 10 cm
So, Radius (r) = 10/2 = 5cm
Height of the cylinder = 12cm.
![volume \: of \: the \: cylinder \: = \pi {r}^{2} h](https://tex.z-dn.net/?f=volume%20%5C%3A%20of%20%5C%3A%20the%20%5C%3A%20cylinder%20%5C%3A%20%20%3D%20%20%5Cpi%20%7Br%7D%5E%7B2%7D%20h)
![= > \pi \times {5}^{2} \times 12 {cm}^{3} = 300\pi {cm}^{3}](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20%5Cpi%20%5Ctimes%20%20%7B5%7D%5E%7B2%7D%20%5Ctimes%20%2012%20%7Bcm%7D%5E%7B3%7D%20%20%20%3D%20300%5Cpi%20%7Bcm%7D%5E%7B3%7D%20)
Radius of the cone = 5 cm.
Height of the cone = 12 cm.
![slant \: height \: of \: the \: cone \: = \sqrt{ {h}^{2} + \: {r}^{2} }](https://tex.z-dn.net/?f=slant%20%5C%3A%20height%20%5C%3A%20of%20%5C%3A%20the%20%5C%3A%20cone%20%5C%3A%20%20%3D%20%20%5Csqrt%7B%20%7Bh%7D%5E%7B2%7D%20%20%2B%20%5C%3A%20%20%7Br%7D%5E%7B2%7D%20%7D%20)
![= > \sqrt{ {5}^{2}+{12}^{2} } cm \: = 13cm](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20%20%5Csqrt%7B%20%7B5%7D%5E%7B2%7D%2B%7B12%7D%5E%7B2%7D%20%7D%20cm%20%5C%3A%20%20%3D%2013cm)
Volume of the cone = 1/3 *πr^2h
![= > \frac{1}{3} \pi \times {5}^{2} \times 12 {cm}^{3} = 100\pi {cm}^{3}](https://tex.z-dn.net/?f=%20%3D%20%20%3E%20%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%5Ctimes%20%20%7B5%7D%5E%7B2%7D%20%20%20%5Ctimes%2012%20%7Bcm%7D%5E%7B3%7D%20%20%3D%20100%5Cpi%20%7Bcm%7D%5E%7B3%7D%20)
therefore, the volume of the remaining solid
![= 300\pi {cm}^{3} - 100\pi {cm}^{3} \\ = 200 \times 3.14 {cm}^{3} = 628 {cm}^{3}](https://tex.z-dn.net/?f=%20%3D%20300%5Cpi%20%7Bcm%7D%5E%7B3%7D%20%20-%20100%5Cpi%20%7Bcm%7D%5E%7B3%7D%20%20%5C%5C%20%20%3D%20200%20%5Ctimes%203.14%20%7Bcm%7D%5E%7B3%7D%20%20%3D%20628%20%7Bcm%7D%5E%7B3%7D%20)
Curved surface of the cylinder =
![2\pi \: rh \: = 2\pi \times 5 \times 12 {cm}^{2} \\ = 120\pi {cm}^{2} .](https://tex.z-dn.net/?f=2%5Cpi%20%5C%3A%20rh%20%5C%3A%20%20%3D%202%5Cpi%20%5Ctimes%205%20%5Ctimes%2012%20%7Bcm%7D%5E%7B2%7D%20%20%5C%5C%20%20%3D%20120%5Cpi%20%7Bcm%7D%5E%7B2%7D%20.)
![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}](https://tex.z-dn.net/?f=curved%20%5C%3A%20surface%20%5C%3A%20of%20%5C%3A%20the%20%5C%3A%20cone%20%5C%3A%20%20%3D%20%5Cpi%20%5C%3A%20rl%20%5C%5C%20%20%3D%20%5Cpi%20%5Ctimes%205%20%5Ctimes%2013%20%7Bcm%7D%5E%7B2%7D%20%20%5C%5C%20%20%3D%2065%5Cpi%20%7Bcm%20%7D%5E%7B2%7D%20%5C%5C%20area%20%5C%3A%20of%20%5C%3A%20%28upper%29circular%20%5C%3A%20base%20%5C%3A%20%5C%5C%20%20of%20%5C%3A%20cylinder%20%5C%3A%20%20%3D%20%20%5C%5C%20%3D%20%20%5Cpi%20%5C%3A%20%20%7Br%7D%5E%7B2%7D%20%20%3D%20%5Cpi%20%5Ctimes%20%20%7B5%7D%5E%7B2%7D%20)
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
![= 120\pi {cm}^{2} + 65\pi {cm }^{2} + 25 \pi {cm}^{2} \\ = 210 \times 3.14 {cm}^{2} = 659.4 {cm}^{2}](https://tex.z-dn.net/?f=%20%3D%20120%5Cpi%20%7Bcm%7D%5E%7B2%7D%20%20%2B%2065%5Cpi%20%7Bcm%20%7D%5E%7B2%7D%20%20%2B%2025%20%5Cpi%20%7Bcm%7D%5E%7B2%7D%20%20%5C%5C%20%20%3D%20210%20%5Ctimes%203.14%20%7Bcm%7D%5E%7B2%7D%20%20%3D%20659.4%20%7Bcm%7D%5E%7B2%7D%20)
<h3>Hope it helps you!!</h3>