Answer:
[tex]V=35.4 in^3[/tex]
Step-by-step explanation:
The volume of a right circular cone is given by the formula,
[tex]V=\frac{1}{3} \pi r^2h[/tex]
where [tex]h=19.4 in[/tex] is the height of the cone.
We can deduce the radius from the circumference of the cone.
[tex]C=2\pi r[/tex]
It was given that the circumference is 8.3 in.
[tex]\Rightarrow 8.3=2(3.14) r[/tex]
[tex]\Rightarrow 8.3=6.28r[/tex]
[tex]\Rightarrow 1.32=r[/tex]
The volume of the cone now becomes;
[tex]V=\frac{1}{3} \times 3.14\times (1.32)^2\times 19.4[/tex]
[tex]V=35.380in^3[/tex]
The volume of the cone to the nearest tenth is 35.4 cubic inches to the nearest tenth.
