A concrete pedestal

A concrete pedestal has the shape of a right circular cone and a height of 2.5 feet. The diameters of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the pedestal's lateral surface area, total surface area, and volume.

Correct answer:

S₃ =  33.836 ft²
S =  60.5395 ft²
V =  32.0704 ft³

Step-by-step explanation:

$$\begin{gathered} h=2.5\text{ft} \\ {D}_1=3\text{ft} \\ {D}_2=5\text{ft} \\ r=D_1/2=3/2=\frac{3}{2}=1.5\text{ft} \\ R=D_2/2=5/2=\frac{5}{2}=2.5\text{ft} \\ {l}^2=h^2+(R-r{)}^2 \\ l=\sqrt{h^2+(R-r{)}^2}=\sqrt{2.5^2+(2.5-1.5{)}^2}\doteq 2.6926\text{ft} \\ {S}_3=\pi \cdot l\cdot (r+R)=3.1416\cdot 2.6926\cdot (1.5+2.5)=33.836{\text{ft}}^2 \end{gathered}$$

$$\begin{gathered} S_1=\pi \cdot r^2=3.1416\cdot 1.5^2\doteq 7.0686{\text{ft}}^2 \\ {S}_2=\pi \cdot R^2=3.1416\cdot 2.5^2\doteq 19.635{\text{ft}}^2 \\ S=S_1+S_2+S_3=7.0686+19.635+33.836=60.5395{\text{ft}}^2 \end{gathered}$$

$V=\frac{1}{3}\cdot \pi \cdot h\cdot (r^2+r\cdot R+R^2)=\frac{1}{3}\cdot 3.1416\cdot 2.5\cdot (1.5^2+1.5\cdot 2.5+2.5^2)=32.0704{\text{ft}}^3$

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