Question

A cylinder is of height 31 cm and base radius 7 cm. A
'hemisphere of radius equal to base radius of cylinder
is cut off from one end and a cone of maximum height
from remaining part is also cut off. The curved
surface area of the remaining part is
(a) 506 cm2
(b) 508 cm2
(c) 510 cm2
(d) 512 cm2
Answer quickly plz with explanation​

Answer 1

Answer:

given H= 31cm

radius R= 7 cm

Step-by-step explanation:

remaining surface area = (2 pi . R.H + 2 pi R^ 2) - [Pi (R+H^2+R^2)] - 2pi R^2

= 1671.33 - 852.33-308

= 510 cm2

Answer 2

Given: Height of the cylinder$=31 cm$, Radius of the cylinder$=7 cm$.

To find: curved surface area of the remaining part.

Solution:

Know that from the question, from the cylinder a hemisphere of same base radius as of the cylinder and a cone maximum remaining height is cut out.

Find the surface area of the remaining part.

Area of the remaining part $=$  Surface Area of the cylinder $-($Surface of the

                                                   hemisphere $+$ Surface area of the cone.

                                             $\[ = 2\pi rh + 2\pi {r^2} - \left[ {\left( {\pi \left( {r + {h^2} + {r^2}} \right)} \right) + 2\pi {r^2}} \right]\]$

                                             $\[\begin{array}{l} = 2 \times \frac{{22}}{7} \times 7 \times 31 + 2 \times \frac{{22}}{7} \times 7 \times 7\\\,\,\,\,\, - \left[ {\frac{{22}}{7}\left( {7 + {{24}^2} + {7^2}} \right) + 2 \times \frac{{22}}{7} \times {7^2}} \right]\end{array}\]$

                                             $\[\begin{array}{l} = 1671.33 - 852.33 - 308\\ = 510c{m^2}\end{array}\]$

Therefore, the curved surface area of the remaining part is $\[510c{m^2}\]$.

Hence, the correct answer is option (c). i.e., $\[510c{m^2}\]$.