Question

The diagram shows the cross-section ABCD of a sculpture in the shape of

a prism
with perpendicular height 9 cm.
AB = 14 cm, CD = 8cm, AD = 12cm and BC = 10cm
The height of the prism is also 9 cm.
What is the volume of the sculpture in cm3?

Answer 1

891 cm³

Explanation:

The volume (V) of the prism is calculated as

V = Ah ( A is the area of cross- section and h is the height (

The cross- section is a trapezium with area (A) calculated as

A =
`(1)/(2)` h ( a + b)

where h is the perpendicular height and a, b the parallel bases

Here h = 9, a = AB = 14 and b = CD = 8 , thus

A =
`(1)/(2)` × 9 × (14 + 8) = 4.5 × 22 = 99 cm² , thus

V = 99 × 9 = 891 cm³