Cone and the ratio

The rotational cone has a height 43 cm, and the ratio of the base surface to lateral surface is 5: 7. Calculate the surface of the base and the lateral surface.

Correct answer:

S₁ =  6050.84 cm²
S₂ =  8471.17 cm²

Step-by-step explanation:

$$\begin{gathered} v=43 \\ {S}_1=\pi r^2 \\ {S}_2=\pi rs \\ {S}_1:S_2=5:7=5/7 \\ \frac{\pi r^2}{\pi rs}=5/7 \\ r/s=5/7 \\ s=r\cdot 7/5 \\ {s}^2=v^2+r^2 \\ {r}^2\cdot 7^2/5^2=43^2+r^2 \\ {r}^2=\frac{1849}{1.96-1} \\ {r}^2=1926.042 \\ r=\sqrt{1926.042}=43.89cm \\ s=r\cdot 7/5=61.44cm \\ {S}_1=\pi r^2=\pi 43.89^2=6050.84{\text{cm}}^2 \end{gathered}$$

$S_2=\pi rs=\pi \cdot 43.89\cdot 61.44=8471.17{\text{cm}}^2$

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