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A cone of maximum size is carved out from a cube of edge 14 cm. Find the surface area of the remaining solid after the cone is carved out.

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1300.34 {cm}^{3}

1364.04 {cm}^{3}

1366.35 {cm}^{3}

1368.30 {cm}^{3}

answer is C.

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Detailed Solution

Given,
Height of the cone h= 14 cm
Radius of the cone r = 14/2 = 7 cm
We know that slant height

l = \sqrt{r^{2} + h^{2}}

= \sqrt{} (7)^{2} + (14)^{2}

= \sqrt{49} + 196

= \sqrt{245}

Now, we calculate surface area of the cone

= π r^{2} + πrl

= (\frac{22}{7}) (7) (\sqrt{2} 25) + (\frac{22}{7}) (7)^{2}

= 22 (\sqrt{245}) + 22 (7)

= 22 (\sqrt{245} + 7)

= 22 (15.65 + 7)

= 22 (22.65)

= 498.35 {cm}^{2}

We know that the surface area of a cube

= 6 (side)^{2}

then,

= 6 (14)^{2}

= 6 (196)

= 1176 {cm}^{2}

Now we have to calculate the solid remaining surface area
Total surface area of cube - Area of circle where cone carved out + curved surface area of cone.

= 1176 - \frac{22}{7} \times 7^{2} + 344.3544

= 1366.35 {cm}^{2}

Hence the surface area of the remaining solid after the cone is carved out =

1366.35 {cm}^{2}

Correct option is 3.

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