A cone is 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.
A cone is 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.
The cone will have a diameter of 14 cm14~cm14 cm and height of 14 cm.14~cm.14 cm. (Radius =7 cm= 7~cm=7 cm)
Slant height of cone, l=r2+h2=(72+142)=15.652 cml=\sqrt{r^2+h^2}=\sqrt{(7^2 + 14^2)} =15.652~cml=r2+h2=(72+142)=15.652 cm
Total Surface area of Cone =πrl+πr2=227×7×15.652+227×72=498.35 cm2= \pi rl + \pi r^2= \dfrac{22}{7}\times7\times15.652 + \dfrac{22}{7}\times7^2 = 498.35~cm^2=πrl+πr2=722×7×15.652+722×72=498.35 cm2
Surface area of solid remaining solid = Total surface area of the cube - area of circle where the cone was carved out + curved surface area of cone (hole remaining in the cube)
=6×14×14−227×72+227×7×15.652= 6\times14\times14 - \dfrac{22}{7}\times7^2 + \dfrac{22}{7}\times7\times15.652=6×14×14−722×72+722×7×15.652
=1366.344 cm2=1366.344~cm^2=1366.344 cm2
Therefore, the surface area of the remaining solid is 1366.344 cm2
The cone will have a diameter of 14 cm14~cm14 cm and height of 14 cm.14~cm.14 cm. (Radius =7 cm= 7~cm=7 cm)
Slant height of cone, l=r2+h2=(72+142)=15.652 cml=\sqrt{r^2+h^2}=\sqrt{(7^2 + 14^2)} =15.652~cml=r2+h2=(72+142)=15.652 cm
Total Surface area of Cone =πrl+πr2=227×7×15.652+227×72=498.35 cm2= \pi rl + \pi r^2= \dfrac{22}{7}\times7\times15.652 + \dfrac{22}{7}\times7^2 = 498.35~cm^2=πrl+πr2=722×7×15.652+722×72=498.35 cm2
Surface area of solid remaining solid = Total surface area of the cube - area of circle where the cone was carved out + curved surface area of cone (hole remaining in the cube)
=6×14×14−227×72+227×7×15.652= 6\times14\times14 - \dfrac{22}{7}\times7^2 + \dfrac{22}{7}\times7\times15.652=6×14×14−722×72+722×7×15.652
=1366.344 cm2=1366.344~cm^2=1366.344 cm2
Therefore, the surface area of the remaining solid is 1366.344 cm2
