The surface area of the cone shown in the figure, for which Jane incorrectly finds the volume, is 74.33 cm².
What is of volume of cone?
Volume of cones the amount of quantity, which is obtained by the solid or object in the 3 dimensional space.
Volume of cone can be given as,
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
Here, (r) is the radius of the base of the cone and (h) is the height of the cone.
The height of the cone is 6.5 cm and the radius is 2.5 cm. Put the values in the above formula,
[tex]V=\dfrac{1}{3}\pi r^2h\\V=\dfrac{1}{3}\pi (2.5)^2(6.5)\\V=\dfrac{1}{3}\pi (6.25)^2(6.5)\\V=\dfrac{40.625\pi }{3}\\V\approx42.5\rm\;cm^3[/tex]
The surface area of cone can be find out by the following formula,
[tex]A=\pi r(r+\sqrt{h^2+r^2})[/tex]
Again put the values in this formula,
[tex]A=\pi \times2.5(2.5+\sqrt{(6.5)^2+(2.5)^2})\\A=\pi \times2.5(2.5+\sqrt{48.5})\\A=\pi \times2.5(2.5+6.96)\\A=\pi \times2.5(9.46)\\A=74.33\rm\; cm^2[/tex]
Thus, the surface area of the cone shown in the figure, for which Jane incorrectly finds the volume, is 74.33 cm².
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