# 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:

*Height
*Volume of the cone

Result

r =  3.501 cm
h =  9.899 cm
V =  127.059 cm3

#### Solution:

$s=10.5 \ \text{cm} \ \\ S_{1}=115.5 \ \text{cm}^2 \ \\ \ \\ S_{1}=\pi \cdot \ r \cdot \ s \ \\ \ \\ r=\dfrac{ S_{1} }{ \pi \cdot \ s }=\dfrac{ 115.5 }{ 3.1416 \cdot \ 10.5 } \doteq 3.5014 \doteq 3.501 \ \text{cm}$
$s^2=h^2 + r^2 \ \\ \ \\ h=\sqrt{ s^2-r^2 }=\sqrt{ 10.5^2-3.5014^2 } \doteq 9.8991 \doteq 9.899 \ \text{cm}$
$S_{2}=\pi \cdot \ r^2=3.1416 \cdot \ 3.5014^2 \doteq 38.5065 \ \text{cm}^2 \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S_{2} \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 38.5065 \cdot \ 9.8991 \doteq 127.0586 \doteq 127.059 \ \text{cm}^3$ Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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