A cube has side lengths of 15 cm. If a hole is drilled from one corner straight through the centre and out the other side, what is the length of the hole?
21.21 cm
25.98 cm
27.65 cm
12.99 cm
To find the length of the hole, we can use the Pythagorean theorem. The length of the hole would be the hypotenuse of a right triangle with sides equal to the diagonal of a face of the cube (15 cm) and the diagonal of the cube (which is also the longest diagonal that passes through the center of the cube).
The length of the diagonal of a face of the cube can be found using the Pythagorean theorem: let's call it "d1".
d1 = √(15^2 + 15^2)
d1 = √(225 + 225)
d1 = √450
d1 ≈ 21.21 cm
The length of the longest diagonal of the cube can be found by using the Pythagorean theorem with three dimensions: let's call it "d2".
d2 = √(15^2 + 15^2 + 15^2)
d2 = √(225 + 225 + 225)
d2 = √675
d2 ≈ 25.98 cm
Therefore, the length of the hole drilled through the cube is approximately 25.98 cm. So the correct answer is:
25.98 cm