Question

The volume of this cone is 140 cm3

Find the perpendicular height, c.
Give your answer rounded to 1 DP.
х
7 cm

Answer 1

x ≈ 3.6 cm

Explanation:

the volume (V) of a cone is calculated as

V = πr²h ( r is the radius and h the perpendicular height )

here diameter = 7 , so r = 7 ÷ 2 = 3.5 , V = 140 and h = x , then

π × 3.5² × x = 140

π × 12.25x = 140 ( divide both sides by 12.25π )

x =
`(140)/(12.25\pi )` ≈ 3.6 cm ( to 1 dec. place )

Answer 2

x = 10.9 cm

Explanation:

Formula for a cone

• Volume (cone) = 1/3 × π × (radius)² × height

Here, we are given :

1. Diameter = 7 cm
2. Volume = 140 cm³

Solving

• 140 = 1/3 × 22/7 × (7/2)² × (x)
• 420 = 11 × 7/2 × (x)
• 77x = 840
• x = 840/77
• x = 10.9 cm (1 DP)