Volumes and Surface Areas of Pyramids, Cones and Spheres

The lateral faces of a pyramid are always triangular.

• True

• False

Answer explanation

The statement is True because the lateral faces of a pyramid are always triangular, forming the sides that connect the base to the apex.

A rectangular pyramid has four identical lateral faces.

• True

• False

Answer explanation

A rectangular pyramid has a rectangular base and four triangular lateral faces. Since the lateral faces are not identical, the statement is false.

A square-based pyramid has how many faces in total?

• 4

• 5

• 6

• 8

Answer explanation

A square-based pyramid has a square base and four triangular faces that meet at a point. Therefore, it has a total of 5 faces: 1 base face and 4 triangular faces.

What is the shape of the base of a hexagonal pyramid as shown?

• Square

• Pentagon

• Hexagon

• Heptagon

Answer explanation

The base of a hexagonal pyramid is a hexagon, which is a six-sided polygon. Therefore, the correct answer is hexagon.

Which part of a pyramid connects the apex (or known as the tip) to the centre of the base?

• Height

• Slant height

• Edge

• Radius

Answer explanation

The height of a pyramid is the perpendicular distance from the apex to the center of the base. It connects these two points directly, making it the correct answer.

Which of the following is used to find the volume of a pyramid?

• Base Area × Height

In a pyramid, what does the term ‘slant height’ refer to?

• The height from the tip to the centre of the base

• The diagonal of the base

• The height along the lateral face

• The total height of all lateral faces

Answer explanation

In a pyramid, 'slant height' refers to the height along the lateral face, which is the distance from the apex to the midpoint of a side of the base. This distinguishes it from other height measurements.

The base of a cone is a:

• Triangle

• Square

• Circle

• Rectangle

Answer explanation

The base of a cone is a circle. This is because a cone is formed by rotating a right triangle around one of its legs, resulting in a circular base.

Which of the following is the net of a cone?

• 
• 
• 
• 

Which formula is used to find the volume of a cone?