Question

26. A cone of height 32 cm and radius 8 cm is made up of clay. A child reshapes it in form of a
sphere. Find the radius of the sphere.​

Answer 1

Given Question :-

• A cone of height 32 cm and radius 8 cm is made up of clay. A child reshapes it in form of a sphere. Find the radius of the sphere.

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☆Answer

☆Given :-

• A cone of height 32 cm and radius 8 cm.
• Come reshapes in the form of a sphere.

☆To Find :

• The radius of the sphere.

☆Formula used :-

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

where

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

${{ \boxed{\large{\bold\red{Volume_{(Sphere)}\: = \: \dfrac{4}{3} \pi r^3}}}}}$

where,

• r = radius of sphere.

☆Solution :-

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

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

$\bf \:\large \red{According \: to \: statement } ✍$

$\bf \: ⟼Height \: of \: cone, \: h = 32 \: cm$

$\bf \:  ⟼ Radius \: of \: cone, r = 8 \: cm$

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

${{ {{\bold{Volume_{(Cone)}\: = \dfrac{1}{3} \times \pi \times (8)^2 \times 32 }}}}} \:\sf \: ⟼(1)$

$\bf \:Let \: Radius \: of \: sphere \: be \: R \: cm$

${{ {{\bold\red{Volume_{(Sphere)}\: = \:\dfrac{4 }{3} \pi R^3}}}}} \: \sf \: ⟼(2)$

⟼ Since, cone is reshapes in the form of sphere.

$\bf\implies \:{\bold\red{Volume_{(Cone)}}} = \:{\bold\red{Volume_{(sphere)}}}$

$\bf\implies \:\dfrac{1}{3} \times \pi \: \times {8}^{2} \times 32 = \dfrac{4}{3} \times \pi \times {R}^{3}$

$\bf\implies \: {R}^{3} = 8 \times 8 \times 8$

$\bf\implies \: {R}^{3} = {8}^{3}$

$\bf\implies \:R = 8 \: cm$

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$\begin{gathered}\Large{\bold{\purple{\underline{More \: InFoRmAtIoN\::}}}} \\ \end{gathered}$

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length²+breadth²)

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