Q8 The diameter of a cone is 10cm
and height is 12 cm calculate the
volume of the cone *
A) 1580 cubic cm
O A
O
O
B) 314.28 cubic cm
C) 2580 cubic cm
O D) 282.85 cubic cm
Answers
Step-by-step explanation:
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Answer:
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}}Radius(r)=
2
Diameter
\longrightarrow⟶ \sf{Radius\:(r)\:=\:\dfrac{12}{2}}Radius(r)=
2
12
\longrightarrow⟶ \sf{Radius\:(r) =6\:cm}Radius(r)=6cm
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}l
2
=r
2
+h
2
\longrightarrow⟶ \sf{(10)^2=(6)^2+h^2}(10)
2
=(6)
2
+h
2
\longrightarrow⟶ \sf{100=36+h^2}100=36+h
2
\longrightarrow⟶ \sf{100-36=h^2}100−36=h
2
\longrightarrow⟶ \sf{64=h^2}64=h
2
\longrightarrow⟶ \sf{h=\sqrt{64}}h=
64
\longrightarrow⟶ \sf{h=8}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}}}}
Volume
cone
=
3
1
πr
2
h
Block in the data,
\sf{Volume_{cone}\:=\:\dfrac{1}{3}\:\times\:\dfrac{22}{7}\:\times\:6\:\times\:6\:\times\:8}Volume
cone
=
3
1
×
7
22
×6×6×8
\sf{Volume_{cone}\:=\:\dfrac{22}{7}\:\times\:2\:\times\:6\:\times\:8}Volume
cone
=
7
22
×2×6×8
\longrightarrow⟶ \sf{Volume_{cone}\:=\:\dfrac{22}{7}\:\times\:12\:\times\:8}Volume
cone
=
7
22
×12×8
\longrightarrow⟶ \sf{Volume_{cone}\:=\:\dfrac{22}{7}\:\times\:96}Volume
cone
=
7
22
×96
\longrightarrow⟶ \sf{Volume_{cone}\:=\:\dfrac{2112}{7}}Volume
cone
=
7
2112
\longrightarrow⟶ \sf{Volume_{cone}\:=\:301.71}Volume
cone
=301.71