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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 cone and of the remaining solid left out after the cone is carved out

Solution:

Given, a cube of edge 14 cm

A cone of maximum size is carved out from the cube.

We have to find the surface area of the cone and remaining solid left out after the cone is carved out.

Height of cone will be 14cm

Radius of cone will be 14/2 = 7 cm

Slant height, l = √r² + h²

= √(7)² + (14)²

= √49 + 196

= √245

Surface area of cone = πrl + πr²

= (22/7)(7)(√245) + (22/7)(7)²

= 22(√245) + 22(7)

= 22(√245 + 7)

= 22(15.65 + 7)

= 22(22.65)

= 498.35 cm²

We know that

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)

Surface area of cube = 6(side)²

= 6(14)²

= 6(196)

= 1176 cm²

Curved surface area of cone (hole remaining in the cube) = 22/7 x 7 x √245 = 344.3544 cm²

Substituting all the values

Surface area of the remaining solid = 1176 - 22/7 x 7² + 344.3544

= 1366.35 cm²

Therefore, the surface area of the remaining solid is 1366.35 cm²

✦ Try This: A sphere of maximum size is carved out from a cube of edge 15 cm. Find the volume of the sphere and volume of the remaining solid left out after the sphere is carved out.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.3 Sample Problem 1

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

Summary:

A cone of maximum size is carved out from a cube of edge 14 cm. The surface area of the cone is 498.35 cm². The surface area of the remaining solid left after the cone is carved out is 1366.35 cm²

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