1.

The height of a solid cylinder is 8 cm and its base radius is 6 cm, a cone of equal height and the radius is extracted from the cylinder, then find the total surface area of the remaining solid.1). 6π cm22). 36π cm23). 216π cm24). 16π cm2

Answer»

Solution;

GIVEN:

HEIGHT of the cylinder, $H = 8$ cm

Base radius of the cylinder, $r = 6$ cm

Radius of the CONE,$r = 6$ cm 

Height of the cone, $h = 8$ cm

Therefore, slant height $l^2 = h^2 + r^2$

$l^2 = 8^2 + 6^2$

$l^2 = 64 + 36$

$l^2 = 100$

$l = (100)^{1/2}$

Slant height, $l = 10$ cm

TSA of remaining solid

= CSA of cylinder + Area ofbase of cylinder + CSA of cone

 $= 2 \pi r h + \pi r^2 + \pi r l$

$= \pi r [ 2h + r + l ]$

$= \pi 6 [ 2×8 + 6 + 10 ]$

$ =\pi 6 [ 16 + 16 ]$

$= \pi( 6 × 32)$

$= 192 \pi$ sq.cm.



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