Question

A cube of 4 cm edge is carved out from a conical wooden block of 10cm diameter and 8 cm height. Find the total surface area that is left out.​

Answer 1

Given,

length of each edge of cube = 4 cm

diameter of conical wooden block = 10 cm

height of conical wooden block = 8 cm

To find,

The remaining surface area of the conical wooden block, after carving out the cube.

Solution,

First of all we have to calculate, the initial surface area of the conical wooden block.

Radius of the cone = 10/2 = 5 cm

Slant height = ✓(5)²+(8)² = ✓25+64 = ✓89 = 9.43 cm (approx)

Curved surface area = 22/7 × 5 × 9.43 = 148.18 cm²

Base area = 22/7 × (5)² = 78.57 cm²

Total surface area = (148.18+78.57) = 226.75 cm²

Base area of cube = (4×4) = 16 cm²

Reduced surface area of conical block = (226.75-16) = 210.75 cm²

Increased surface area of conical block = 210.75+(16×3) = 258.75 cm²

Hence, the remaining surface area will be 258.75 cm².