Q) From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and same radius is hollowed out. Find the total surface area of the remaining solid.

Ans: Let’s draw the diagram to capture the shape:

After taking out the conical shape from cylinder, total surface area of the remaining solid will be:

= Curved surface area of the cylinder + One side base area of the cylinder + Curved surface area of cone

(Note, here one side of the base is removed in the cavity)

= 2 r h + r²  + r l

= r  (2 h + r  + l ) …………. (i)

Here, it is given that height of the cylinder, h = 30 cm

radius of the cylinder, r = 7 cm

The slant height of the cone =   = 25 cm

By transferring these values in the equation (i), we get:

Total Surface area of the remaining solid  = 7 [ 2 x 30 + 7 + 25]  

= 644

=  (644)

= 2024 cm²

Therefore, the surface area of the remaining solid is 2024 cm².

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