The diagram 2

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

*Base Radius
*Height
*Volume of the cone

Correct answer:

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

Step-by-step explanation:

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

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

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

Try another example