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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 |
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Answer» Solution; 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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