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The volume of this cone is 140 cm3
Find the perpendicular height, c.
Give your answer rounded to 1 DP.
х
7 cm

The volume of this cone is 140 cm3 Find the perpendicular height c Give your answer rounded to 1 DP х 7 cm class=

Respuesta :

Answer:

x = 10.9 cm

Step-by-step 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)

Answer:

x ≈ 3.6 cm

Step-by-step 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 = [tex]\frac{140}{12.25\pi }[/tex] ≈ 3.6 cm ( to 1 dec. place )