Question

There is a cuboid with length half of the edge of a cube. The breadth & height of this cuboid is half of its length. Find the ratio of the curved surface area of cube to cuboid. what is the formula of lateral surface area of cylinder

Answer 1

8:2

Step-by-step explanation:

Let the edge of cube be 'x'

Then,

Length of cuboid = ˣ/₂

Breadth = ˣ/₂ × ¹/₂ = ˣ/₄

Height = ˣ/₂ × ¹/₂ = ˣ/₄

We know that, Curved surface area and Lateral surface area are same.

$\large\red{\underline{{\boxed{\textbf{lateral\: Surface\:Area\:of\: Cuboid\: = 2h(l + b)}}}}}$

• In which h is height, l is length and b is breadth.

Now, Put the values

⇒2h(l + b)

⇒2 × ˣ/₄( ˣ/₂ + ˣ/₄)

⇒ˣ/₂ ( ˣ/₂ + ˣ/₄)

⇒x²/₄ + x²/₈

⇒x²+x² /₈

⇒2x²/₈

$\large\purple{\underline{{\boxed{\textbf{lateral\: Surface\:Area\:of\: Cube\: = 4a²}}}}}$

• In which a is edge of cube.

Now, put the value.

⇒ 4a²

⇒ 4(x)²

⇒ 4x²

Ratio's of curved surface area's of cube and cuboid is

$⇒ \frac{ \frac{2 {x}^{2} }{8} }{4 {x}^{2} }$

$⇒ \frac{8}{2}$

⇒8:2

Hence the ratio is 8 : 2.

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Curved surface area of cylinder = 2πrh