# 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:

$s=10.5 \ \text{cm} \ \\ S_{1}=115.5 \ \text{cm}^2 \ \\ \ \\ S_{1}=\pi \cdot \ r \cdot \ s \ \\ \ \\ r=\dfrac{ S_{1} }{ \pi \cdot \ s }=\dfrac{ 115.5 }{ 3.1416 \cdot \ 10.5 } \doteq 3.5014 \doteq 3.501 \ \text{cm}$
$s^2=h^2 + r^2 \ \\ \ \\ h=\sqrt{ s^2-r^2 }=\sqrt{ 10.5^2-3.5014^2 } \doteq 9.8991 \doteq 9.899 \ \text{cm}$
$S_{2}=\pi \cdot \ r^2=3.1416 \cdot \ 3.5014^2 \doteq 38.5065 \ \text{cm}^2 \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ S_{2} \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 38.5065 \cdot \ 9.8991 \doteq 127.0586 \doteq 127.059 \ \text{cm}^3$

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