Question

This solid is a triangular prism with a cylinder removed. Find the volume of the solid to 1 d.p.

Answer 1

V ≈ 571.5 cm³

Explanation:

the volume (V) of the solid is calculated as

V = volume of prism - volume of cylinder

volume of prism = area of triangular end × length

=
`(1)/(2)` × 11.1 × 10 × 11.8 = 654.9 cm³

volume of cylinder = πr² l ( r is the radius and l the length )

here diameter = 3 cm then r = 0.5 × 3 = 1.5 cm

volume of cylinder = π × 1.5² × 11.8 ≈ 83.41 cm³

then

V = 654.9 - 83.41 = 571.5 cm³ ( to 1 dec. place )

Answer 2

571.5cm^3

Explanation:

first calculate the total volume

formula of a triangle-height×base/2

10×11.1/2=55.5cm^2

times it by the height=654.9cm^3

minus the volume of the cylinder

=height×radius^2×pi

radius=1.5

therefore volume of cylinder=83.4cm^3

total-cylinder=volume

654.9-83.4=571.5cm^3