Question

if a cylinder and cone have the same base radius and height then the volume of a cylinder is doubled that of cone

true or false​

Answer 1

Answer:

false

Step-by-step explanation:

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Answer 2

$\bf \:\large \blue{Given \: Question}$

• If a cylinder and cone have the same base radius and height then the volume of a cylinder is doubled that of cone. State True or False.

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$\huge \orange{AηsωeR}$

$\large \red{\sf \: Given :- }$

• A cylinder and cone have the same base radius and height.

$\large\green{\bf \: To  \: Find :- }$

• State True or False. The volume of a cylinder is doubled that of cone.

$\begin{gathered}\Large{\bold{\pink{\underline{Formula \: Used \::}}}} \end{gathered}$

${{ \boxed{\large{\bold\green{Volume_{(Cylinder)}\: = \:\pi r^2 h }}}}}$

where,

• r = radius of cylinder
• h = height of cylinder

${{ \boxed{\large{\bold\green{Volume_{(Cone)}\: = \:\dfrac{1}{3} \pi r^2 h }}}}}$

where,

• r = radius of cone
• h = height of cone

$\begin{gathered}\Large{\bold{\pink{\underline{CaLcUlAtIoN\::}}}} \end{gathered}$

$\begin{gathered}\begin{gathered}\bf Let = \begin{cases} &\sf{r \: be \: the \: radius \: of \: cylinder \: and \: cone} \\ &\sf{h \: be \: the \: height \: of \: cylinder \: and \: cone} \end{cases}\end{gathered}\end{gathered}$

$\sf \: ⟼Volume \: of \: cylinder, \: V_1 = \pi \: {r}^{2} h$

$\sf \: ⟼Volume \: of \: cone, \: V_2 =\dfrac{1}{3} \pi \: {r}^{2} h$

$\begin{gathered}\bf\purple{So,} \end{gathered}$

$\sf \: ⟼ \: V_2 = \dfrac{1}{3} V_1$

$\sf \: ⟼V_1 = 3V_2$

☆ Hence, The volume of a cylinder is triple of that of cone.

$\large{\boxed{\boxed{\bf{Hence, \: given \: statement \: is \: false.}}}}$

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$\large \red{\bf \: ⟼ Explore \: more } ✍$

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length ²+breadth ²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²