Question

.A solid piece of iron in the form of a cuboid of dimensions 49cm × 33cm × 24cm, is moulded to form a solid sphere. The radius of the sphere is *
1 point
(a) 21cm
(b) 23cm
(c) 25cm
(d) 19cm​

Answer 1

$\LARGE\textbf{\underline{\underline{Answer :- }}}$

$\boxed{\large\textbf{( a ) 21 cm}}$

$\LARGE\textbf{\underline{Given :- }}$

• Dimensions of the cuboid are = 49cm , 33cm , 24cm.

$\LARGE\textbf{\underline{To find :- }}$

• If the cuboid is moulded in Sphere then what would be the radius of the sphere.

$\LARGE\textbf{\underline{Formulas :- }}$

• $\boxed{\large\textbf{Volume of the cuboid = L × B × H}}$

• $\boxed{\large\textbf{Volume of a Sphere = \cfrac{4}{3} × \pi × r ^{3} }}$

$\LARGE\textbf{\underline{Here :- }}$

• L = LENGTH
• B = BREADTH
• H = HEIGHT
• R = RADIUS
• π = 22/7

$\LARGE\textbf{\underline{Solution :- }}$

⟾ As the cuboid is moulded into the sphere so first we have to find the volume of the cuboid.

• $\large\textbf{Volume of the cuboid = 49 × 33 × 24}$

• $\boxed{\large\textbf{Volume of the cuboid = 38808 cu.cm}}$

⟾ As this volume of the cuboid we have to mould in to the sphere so this volume would also be the volume of the sphere which we have to make.

$\boxed{\therefore\large\textbf{Volume of Sphere = \cfrac{4}{3} × \cfrac{22}{7} × r^{3} }}$

$\therefore\large\textbf{38808 = \cfrac{4}{3} × \cfrac{22}{7} × r^{3} }$

$\therefore\large\textbf{ \cfrac{38808 × 3 × 7}{4 × 22} = r^{3} }$

$\therefore\large\textbf{ 9361 = r^{3} }$

$\therefore\large\textbf{ \sqrt[3]{9361} = r }$

$\boxed{\therefore\large\textbf{21 = r}}$

⟾So the radius of the sphere moulded from the cuboid is 21 cm.

$\LARGE\textbf{\underline{\underline{More Formal:- }}}$

OF CUBOID :-

• $\large\textbf{Lateral surface area = 2H ( L + B)}$

• $\large\textbf{Total surface area = 2 ( LB + BH + HL )}$

• $\large\textbf{ Volume = L × B × H}$

• H = HEIGHT
• B = BREADTH
• L = LENGTH

OF SPHERE :-

• $\large\textbf{Surface area = = 4 × \pi × r^{3} }$

• $\large\textbf{Volume = \cfrac{4}{3} × \pi × r^{3} }$

• r = Radius
• π = 22/7 or 3.14

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