Find the exact volume of a cone 6yd height 5yd base

Accepted Solution

Answer:The exact volume of a cone is 10 yd³.Step-by-step explanation:Given:Height of cone (h) is 6 yd and base (b) is 5 yd.Now, to get the volume we need to find the radius. So, to find radius we put the formula of base:Let the radius be [tex]r[/tex] Base=[tex]\pi r^2[/tex][tex]b=\pi\times r^{2}[/tex][tex]5=\pi\times r^{2}[/tex]Dividing both sides by π and using square root on both the sides:[tex]5\div \pi=(\pi \times r^{2}) \div \pi[/tex][tex]\frac{5}{\pi}=r^{2}[/tex][tex]\frac{5}{\pi}=r^{2}[/tex][tex]r^{2}=\frac{5}{\pi}-----1[/tex]Now, putting the formula for getting the volume (v) of cone:Volume = [tex]\pi r^2\frac{h}{3}[/tex][tex]v=\pi\times r^{2}\times \frac{6}{3}[/tex][tex]v=\pi\times r^{2}\times 2[/tex]Substituting the value of [tex]r^2[/tex] from equation (1), we get:[tex]v=\pi\times \frac{5}{\pi}\times 2[/tex][tex]v=10[/tex] yd³Volume of cone is 10 yd³Therefore, the exact volume of a cone is 10 yd³.