Question

10.

6 cm
8 cm
12 cm
The diagram shows a solid prism made from metal.
The cross-section of the prism is a trapezium.
Calculate the mass of the prism.
Give your answer in kilograms.
The parallel sides of the trapezium are 8 cm and 12 cm.
The height of the trapezium is 6 cm.
The length of the prism is 20 cm.
The density of the metal is 5 g/cm³.
20 cm

Answer 1

Below

Explanation:

Find the area of the trapezium

area x length = volume

volume x density = mass

Area = 6 x (12+8)/2 = 60 cm^2

60 cm^2 x 20 cm = 1200 cm^3 volume

1200 cm^3 * 5 g / cm^3 = 6000 gm

Answer 2

6 kg

Explanation:

For a prism, the volume is

V = Bh

where B = area of the base, and h = height of the prism.

For a trapezium, the area is

A = (b1 + b2)h/2

where b1 and b2 are the lengths of the parallel bases, ad h is the height of the trapezium.

V = (12 cm + 8 cm)(6 cm)/2 × 20 cm = 1200 cm³

density = mass/volume

mass = density × volume

mass = 1200 cm³ × 5 g/cm³

mass = 6000 g × (1 kg)/(1000 g)

mass = 6 kg