Respuesta :
Answer:
[tex]\begin{gathered} Length\text{ of the apex = 0.75 dm} \\ Area\text{ of the base = 50.24 dm}^2 \end{gathered}[/tex]Explanation:
Given:
Volume of the cone = 4π dm³
diameter of the base = 80cm
To find:
a) the length of the apex
b) the base area
A) the apex of a cone is the height of the cone
To get the height, we will apply the formula for the volume of a cone
[tex]\begin{gathered} Volume\text{ of a cone = }\frac{1}{3}πr²h \\ where\text{ r = radius} \\ h\text{ = height} \end{gathered}[/tex]diameter = 80cm
diameter = 2(radius)
radius = diameter/2 = 80/2 = 40cm
The units are different, so we need to do conversion fromcm to dm
1 dm = 10cm
40cm = 40/10 = 4 dm
substitute the values into the formula:
[tex]\begin{gathered} 4π\text{ = }\frac{1}{3}\timesπ\times4^2\times h \\ 3(4π)\text{ = \pi}\times16\times h \\ h\text{ = }\frac{12π}{16π} \\ h\text{ = }\frac{3}{4}dm \\ h\text{ = 0.75 dm} \end{gathered}[/tex]b) The base of a cone is a circle. So, the area of the base will be the area of the circle
[tex]\begin{gathered} Area\text{ of circle = \pi r}^2 \\ let\text{ \pi = 3.14} \\ r\text{ = radius} \end{gathered}[/tex][tex]\begin{gathered} Area\text{ of the circle = 3.14 }\times4^2 \\ \\ Area\text{ of the circle = 50.24 dm} \\ \\ Area\text{ of the base = 50.24 dm}^2 \end{gathered}[/tex]
