Question

The area of the surface of a ball is equal to the area of the curved surface of a right circular cylinder. If both the height and diameter of the cylinder are 12 cm, find the diameter of the ball.
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Answer 1

Answer:

Solve this equation for d.

SA of ball = SA of curve surface of cylinder

4π(d/2)2 = 2π(d/2)(h)

4π(d2 / 4) = dπh

πd2 = dπh

d2 = dh

d2 = 144

d = 12

Answer 2

Concept:

Here, the Concept of Surface area and volume has to be used. We are given that the surface area of a Spherical object is equals to the Area of Curved surface area of Cylinder. Also, the Height and diameter of the Cylinder are equal. Then we have to find the Diameter of Spherical Object.

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Given: The Surface Area of Ball is equal to the Curved surface area of Right Circular Cylinder. Also, Both the Height and Diameter of the cylinder is 12cm

To Find: Diameter of Ball

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Formula to be Used:

$\nrightarrow\sf{Surface\: area\: of\: Sphere=4\times \pi\times {r}^{2}}$$\\ \nrightarrow\sf{Curved\: Surface\: area\: of\: Cylinder= 2\times \pi\times R\times h}$

Where,

• r is Radius of sphere
• h is Height cylinder
• R is Radius of cylinder

Solution:

We are given that, $\\ \leadsto\sf{Surface\: area\: of\: ball=Curved\: surface\: area\: of\: Cylinder}$

So, Using the formula we get, $\\ \rightarrow\sf{Surface\: area\: of\: sphere=Curved\: surface\: area\: of\: cylinder}$

$\rightarrow\sf{4\times \pi\times {r}^{2}=2\times \pi\times R\times h}$

$\rightarrow\sf{4\times \pi\times {r}^{2}=2\times \pi\times R\times 12}$

We know,

$\rightharpoonup\sf{d=2R}$

$\rightharpoonup\sf{12=2R}$

$\rightharpoonup\sf{R=6}$

Now,

$\rightarrow\sf{4\times \pi\times {r}^{2}=2\times \pi\times 6\times 12}$

$\rightarrow\sf{\large{\frac{4\times \pi\times {r}^{2}}{2\times \pi}}=6\times 12}$

$\rightarrow\sf{2\times {r}^{2}=72}$

$\rightarrow\sf{{r}^{2}=\large{\frac{72}{2}}}$

$\rightarrow\sf{{r}^{2}=36}$

$\rightarrow\sf{r=\sqrt{36}}$

$\rightarrow\bold{r=6}$

Now, substituting value of radius in d=2r. We get,

$\implies\sf{d=2\times r}$

$\implies\sf{d=2\times 6}$

$\implies\bold{d=12}$

Required Answer: $\\ \: \: \: \: \: \: \: \: \twoheadrightarrow \sf{\color{red}{Hence,\: The\: Diameter\: of\: Ball\: is\: 12\: cm.}}$