the volume of the cone is 25.12cm cubed, and the area of the base is 12.56cm squared.what is the height

Accepted Solution

Height of the cone having volume as [tex]25.12 \text { cm}^{3}[/tex] and base area [tex]12.56 \text { cm}^{2}[/tex] is 6 cm.Solution:Given that volume of cone = [tex]25.12 \text{ cm}^{3}[/tex]Area of base = [tex]12.56 \text { cm}^{2}[/tex]Need to determine height of the cone.Formula for volume of the cone is as follows[tex]\mathrm{V}_{c}=\frac{1}{3} \pi r^{2}{h} \rightarrow (1)[/tex]Area of circular base of cone = [tex]A_{b}=\pi r^{2}[/tex]Replacing [tex]\pi r^{2} \text { by } A_{b}[/tex] in equation (1), we get[tex]\mathrm{V}_{\mathrm{c}}=\frac{1}{3} \mathrm{A}_{\mathrm{b}} \mathrm{h}[/tex][tex]\Rightarrow \frac{3 \mathrm{V} c}{\mathrm{A}_{\mathrm{b}}}=h[/tex][tex]\Rightarrow h=\frac{3 \mathrm{v} c}{\mathrm{A}_{\mathrm{b}}} \rightarrow (2)[/tex]In our case Volume of cone [tex]V_c= 21.12 \text{ cm}^3[/tex] and Area of base [tex]A_b=12.56 \text { cm}^2[/tex]On substituting the values of volume and area in equation 2 we get[tex]h=\frac{3 \times 25.12}{12.56}=6 \text{ cm }[/tex]