Question

Drag each label to the correct location on the image. Not all labels will be used.2Determine the correct dimensions for the given figures so that the volume of the cone is equal to the volume of the cylinder, and the height ofthe cylinder is times the height of the cone.Figures are not drawn to scale.25 cm20 cm6 cm18 cm15 cm3 cm

Answer 1

Step-by-step explanation

1) The volume of a cylinder is given by:

`V_1=\pi r_1^2\cdot h_1.`

Where r₁ is the radius and h₁ is the height.

2) The volume of a cone is given by:

`V_2=(1)/(3)\pi r_2^2\cdot h_2.`

Where r₂ is the radius and h₂ is the height.

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(1) From the statement, we know that the height of the cylinder (h₁) is 4/3 times the height of the cone (h₂), so we have:

`h_1=(4)/(3)\cdot h_2.`

(2) If the volumes of the cone and the cylinder are equal, we have:

`\begin{gathered} V_1=V_2, \\ r_1^2\cdot h_1=(1)/(3)r_2^2\cdot h_2. \end{gathered}`

(3) Replacing the equation of point (1) in the equation of point (2), we get:

`\begin{gathered} r_1^2\cdot((4)/(3)\cdot h_2)=(1)/(3)r_2^2\cdot h_2, \\ 4r_1^2=r_2^2, \\ (2r_1)^2=r_2, \\ r_2=2r_(1.) \end{gathered}`

So we see that the radius of the cone is two times the radius of the cylinder.

(4) Looking at the length of the statement

i) we see that 6 cm is two times 3 cm, so we identify:

• r₁ = radius of the cylinder = 3 cm,

,

• r₂ = radius of the cone = 2 x 3cm = 6 cm.

ii) we see that 20 cm is 4/3 times 15 cm, so we identify:

• h₁ = height of the cylinder = 20 cm,

,

• h₂ = height of the cone = 15 cm.

Inserting these results into the figures, we get:

Answer