Question

The volume of cone whose slant height is 10 cm and diameter is 12 cm. is.....  

 

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Answer 1

Given :

• Slant height of cone = 10 cm.
• Diameter of cone = 12 cm.

To Find :

• Volume of the cone.

Solution :

We have the diameter of the cone as 12 cm.

Using this first calculate the radius (r) of the cone.

$\longrightarrow$ $\sf{Radius\:(r)\:=\:\dfrac{Diameter}{2}}$

$\longrightarrow$ $\sf{Radius\:(r)\:=\:\dfrac{12}{2}}$

$\longrightarrow$ $\sf{Radius\:(r) =6\:cm}$

We know that volume of the cone is ⅓ times the value of π times the value of r² (in this case 6²) times the value of height (h)

The quantity perpendicular height (h) of the cone is missing.

So, calculating the perpendicular height (h),

$\longrightarrow$ $\sf{l^2=r^2+h^2}$

$\longrightarrow$ $\sf{(10)^2=(6)^2+h^2}$

$\longrightarrow$ $\sf{100=36+h^2}$

$\longrightarrow$ $\sf{100-36=h^2}$

$\longrightarrow$ $\sf{64=h^2}$

$\longrightarrow$$\sf{h=\sqrt{64}}$

$\longrightarrow$ $\sf{h=8}$

•°• Height of the cone = 8 cm.

Now, we have all the required quantities.

Use the formula of volume of cone.

Formula :

$\large{\boxed{\sf{\purple{Volume_{cone}\:=\:\dfrac{1}{3}\:\pi\:r^2\:h}}}}$

Block in the data,

$\sf{Volume_{cone}\:=\:\dfrac{1}{3}\:\times\:\dfrac{22}{7}\:\times\:6\:\times\:6\:\times\:8}$

$\sf{Volume_{cone}\:=\:\dfrac{22}{7}\:\times\:2\:\times\:6\:\times\:8}$

$\longrightarrow$ $\sf{Volume_{cone}\:=\:\dfrac{22}{7}\:\times\:12\:\times\:8}$

$\longrightarrow$ $\sf{Volume_{cone}\:=\:\dfrac{22}{7}\:\times\:96}$

$\longrightarrow$ $\sf{Volume_{cone}\:=\:\dfrac{2112}{7}}$

$\longrightarrow$ $\sf{Volume_{cone}\:=\:301.71}$

$\large{\boxed{\sf{\purple{Volume\:of\:cone\:=\:301.71\:cm^3}}}}$

Answer 2

$\bold\green{\underline{\underline{GIVEN:}}}$

• The slant height of of cone=10cm
• The diameter of cone=12cm

$\bold\orange{\underline{\underline{:SOLUTION:}}}$

• DIAMETER=12cm
• RADIUS=12/2=6cm

$\bold\purple{\boxed{<em>FI</em><em>ND</em><em>-VOLUME</em><em> </em>\:AND \:HEIGHT}}$

• As we know that to find the find the volume of
• cone before we have to find out the height
• because height is missing here

$\bold\purple{\boxed{l^2=r^2+h^2}}$

$⟹ {l}^{2} = {r}^{2} + {h}^{2} \\ \\ ⟹ {10}^{2} = {6}^{2} + {h}^{2} \\ \\ ⟹100 = 36 + {h}^{2} \\ \\ ⟹ {h}^{2} = 100 - 36 \\ \\ ⟹ h = \sqrt{64} = 8cm$

NOW,

• by using formula of volume of cone

$⟹volume = \frac{1}{3} \pi \: {r}^{2} h \\ \\ ⟹volume = \frac{1}{3} \times \frac{22}{7} \times {6}^{2} \times 8 \\ \\ ⟹volume = \frac{22 \times 6 \times 2 \times 8}{7} \\ \\ ⟹volume = 371.71 {cm}^{3}$

$\bold\green{\boxed{VOLUME\:OF\:CONE=371.71\:cm^3}}$