Explanation
1) The volume of a cylinder is given by:
[tex]V_1=\pi r_1^2\cdot h_1.[/tex]
Where r₁ is the radius and h₁ is the height.
2) The volume of a cone is given by:
[tex]V_2=\frac{1}{3}\pi r_2^2\cdot h_2.[/tex]
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:
[tex]h_1=\frac{4}{3}\cdot h_2.[/tex]
(2) If the volumes of the cone and the cylinder are equal, we have:
[tex]\begin{gathered} V_1=V_2, \\ r_1^2\cdot h_1=\frac{1}{3}r_2^2\cdot h_2. \end{gathered}[/tex]
(3) Replacing the equation of point (1) in the equation of point (2), we get:
[tex]\begin{gathered} r_1^2\cdot(\frac{4}{3}\cdot h_2)=\frac{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}[/tex]
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
