Mathematics

Mathematics

Problem

A cube of side 14 cm14\,\text{cm} has a cylindrical hole of radius 3.5 cm3.5\,\text{cm} drilled straight through its centre and perpendicular to one face. Find, to the nearest cubic centimetre, the volume of the remaining solid. a) 2 573 cm32\,573\,\text{cm}^3 b) 2 205 cm32\,205\,\text{cm}^3 c) 2 475 cm32\,475\,\text{cm}^3 d) 2 744 cm32\,744\,\text{cm}^3
Intuitive explanation

The key is to picture what's actually removed: a cylinder passing completely through the cube from one face to the opposite face. Since the cylinder's axis is perpendicular to a face and passes through the cube's center, its height equals the cube's side length. You'll subtract the cylinder's volume from the cube's volume—a straightforward application of Vcube−VcylinderV_{\text{cube}} - V_{\text{cylinder}}, where Vcylinder=πr2hV_{\text{cylinder}} = \pi r^2 h.

Intuitive explanation

The key is to picture what's actually removed: a cylinder passing completely through the cube from one face to the opposite face. Since the cylinder's axis is perpendicular to a face and passes through the cube's center, its height equals the cube's side length. You'll subtract the cylinder's volume from the cube's volume—a straightforward application of Vcube−VcylinderV_{\text{cube}} - V_{\text{cylinder}}, where Vcylinder=πr2hV_{\text{cylinder}} = \pi r^2 h.

Browse the problem library