The diagram 2

The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm². Calculate correct to 3 significant figures:

*Base Radius
*Height
*Volume of the cone

Correct result:

r =  3.5014 cm
h =  9.899 cm
V =  127.0883 cm³

Solution:

$$\begin{gathered} s=10.5\text{ cm } \\ {S}_1=115.5{\text{cm}}^2 \\ {S}_1=\pi \cdot r\cdot s \\ r={\displaystyle \frac{S_1}{\pi \cdot s}}={\displaystyle \frac{115.5}{3.1416\cdot 10.5}}=3.5014\text{ cm} \end{gathered}$$

$$\begin{gathered} s^2=h^2+r^2 \\ h=\sqrt{s^2-r^2}=\sqrt{10.5^2-3.5014^2}=9.899\text{ cm} \end{gathered}$$

$$\begin{gathered} S_2=\pi \cdot r^2=3.1416\cdot 3.5014^2\doteq 38.5155{\text{cm}}^2 \\ V={\displaystyle \frac{1}{3}}\cdot S_2\cdot h={\displaystyle \frac{1}{3}}\cdot 38.5155\cdot 9.899=127.0883{\text{cm}}^3 \end{gathered}$$

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