Geometry — Practice

Question 1

The radius of a circle is 9 cm. Find its diameter.

Accepted Answer

Diameter = 2 x radius = 2 x 9 = 18 cm.

Question 2

Which chord of a circle is the longest?

Accepted Answer

The diameter, because it passes through the centre.

Question 3

How many faces, edges and vertices does a cube have?

Accepted Answer

6 faces, 12 edges and 8 vertices.

Question 4

Name the solid that has no edges and no vertices.

Accepted Answer

A sphere. It has a single curved surface.

Question 5

Find the perimeter of a quadrilateral whose sides are 10 cm, 5 cm, 2 cm and 7 cm.

Accepted Answer

Perimeter = 10 + 5 + 2 + 7 = 24 cm.

Question 6

A rectangle has sides 7 cm, 4 cm, 7 cm and 4 cm. Find its perimeter.

Accepted Answer

Perimeter = 7 + 4 + 7 + 4 = 22 cm.

Question 7

A four-sided figure has all sides equal but its diagonals are of different lengths. Name it and say how it differs from a square.

Accepted Answer

A rhombus. A square also has four equal sides, but a square's diagonals are equal in length while a rhombus's are not.

Question 8

A cube and a cuboid both have 6 faces, 12 edges and 8 vertices. How would you tell them apart?

Accepted Answer

By the faces. All six faces of a cube are equal squares; a cuboid only has its opposite faces equal.

Question 9

Explain why a circle cannot be filled completely with square tiles.

Accepted Answer

A circle is bounded by a curve and a square by straight edges. Straight edges cannot follow a curve, so gaps are always left around the rim.

Question 10

The perimeter of a quadrilateral is 30 cm. Three of its sides measure 8 cm, 6 cm and 9 cm. Find the fourth side.

Accepted Answer

Sum of the three known sides = 8 + 6 + 9 = 23 cm. Fourth side = 30 - 23 = 7 cm.

Practice — Geometry