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Find the lateral surface area and the volume of the object shown below (round to nearest whole number as needed)

Find the lateral surface area and the volume of the object shown below (round to nearest-example-1
User Grigb
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1 Answer

22 votes
22 votes

Lateral Surface Area and Volume of a Cone

Given a cone of radius r and height h, the lateral surface area can be calculated as follows:


A_l=\pi r\sqrt[]{r^2+h^2}

And the volume is:


V=(\pi r^2h)/(3)

The image shows a cone and we are given the diameter of the base and the height.

We need first to calculate the radius of the base:


\begin{gathered} r=(d)/(2) \\ r=\frac{11.4\operatorname{cm}}{2} \\ r=5.7\operatorname{cm} \end{gathered}

Now calculate the lateral surface area:


A_l=\pi\cdot5.7cm\cdot\sqrt[]{(5.7cm)^2+(16.2\operatorname{cm})^2}

Calculating:


A_l=17.907cm\cdot\sqrt[]{32.49cm^2+262.44\operatorname{cm}^2}
\begin{gathered} A_l=17.907cm\cdot\sqrt[]{294.93\operatorname{cm}} \\ A_l=17.907cm\cdot17.17\operatorname{cm} \\ A_l=308\operatorname{cm} \end{gathered}

Rounding to the nearest whole number, the area is 308 square cm

Now for the volume:


V=\frac{\pi(5.7cm)^2(16.2\operatorname{cm})}{3}

Calculating:


\begin{gathered} V=(1653.5396)/(3) \\ V=551\operatorname{cm}^3 \end{gathered}

Rounding to the nearest whole number, the volume is 551 cubic cm

User Thehale
by
2.7k points
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