2. The cylinder and cone has equal base radius and perpendicular height. If the volume of the cylinder 600 cm. find the volume of the cone.
Answers
\huge\sf\pink{Answer}Answer
☞ Volume of cone is 200 cm³
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\huge\sf\blue{Given}Given
✭ A right circular cylinder and a right circular cone have equal base, height & radius
✭ Volume of cylinder = 600 cm³
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\huge\sf\gray{To \:Find}ToFind
◈ Volume of the cone?
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\huge\sf\purple{Steps}Steps
So here we shall just take tthe given value and simply substitute in the other formula, that is,
We know that volume of cylinder is given by,
\underline{\boxed{\sf Volume_{cylinder} = \pi r^2 h}}
Volume
cylinder
=πr
2
h
➝ \sf \red{\pi r^2 h = 600 \ cm^3} \:\:\: -eq(1)πr
2
h=600 cm
3
−eq(1)
So we also know that the volume of a cone is given by,
\underline{\boxed{\sf Volume_{Cone} = \dfrac{1}{3} \pi r^2 h}}
Volume
Cone
=
3
1
πr
2
h
\bigg\lgroup \sf Sub \ Value \ of \ eq(1)\bigg\rgroup
⎩
⎪
⎪
⎪
⎧
Sub Value of eq(1)
⎭
⎪
⎪
⎪
⎫
➝ \sf \dfrac{1}{3}\pi r^2 h
3
1
πr
2
h
➝ \sf \dfrac{1}{3} \times 600
3
1
×600
➝ \sf \orange{Volume_{Cone} = 200 \ cm^3}Volume
Cone
=200 cm
3
\sf \star \: Diagram \: \star⋆Diagram⋆
Cylinder
\setlength{\unitlength}{1 cm} \thicklines \begin{picture}(2,0)\qbezier(0,0)(0,0)(0,2.5)\qbezier(2,0)(2,0)(2,2.5)\qbezier(0,0)(1,1)(2,0)\qbezier(0,0)( 1, - 1)(2,0) \put(2.3,1){\vector(0,1){1.5}}\put(2.3,1){\vector(0, - 1){1.2}}\put(2.3,1){ $\bf h$}\put(0.3,0.1){ $\bf r$}\put(0,0){\vector(1,0){1}}\qbezier(0,2.5)(1,1.5)(2,2.5)\qbezier(0,2.5)(1, 3.5)(2,2.5)\end{picture}
Cone
\setlength{\unitlength}{30} \begin{picture}(20,10) \linethickness{1.2} \qbezier(1,1)(3., 0)(5,1)\qbezier(1,1)(3.,2)(5,1)\put(3,1){\circle*{0.15}}\put(3,1){\line(0,1){3}}\qbezier(1,1)(1,1)(3,4)\qbezier(5,1)(3,4)(3,4)\put(3,1){\line(1,0){2}}\put(3.2,1.1){$ \sf r \: cm $}\put(1.9,1.9){$ \sf height $}\end{picture}
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☯ \sf \large\underline{\sf Know \ More}
Know More
»» \sf Volume \ of \ Sphere = \dfrac{4}{3} \pi r^3Volume of Sphere=
3
4
πr
3
»» \sf Volume \ of \ cuboid = lbhVolume of cuboid=lbh
»» \sf Volume \ of \ cube = a^3Volume of cube=a
3
»» \sf Volume \ of \ Hemisphere = \dfrac{2}{3} \pi r^3Volume of Hemisphere=
3
2
πr
3
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