If the radius of a sphere is increased by 50%, then its surface area will increase by:

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Accepted Answer

Let the original radius of the sphere be $$ r $$. The surface area of a sphere is given by:  
$$
	ext{Surface Area} = 4\pi r^2
$$

When the radius is increased by 50%, the new radius becomes:  
$$
	ext{New Radius} = 1.5r
$$

The new surface area is:  
$$
	ext{New Surface Area} = 4\pi (1.5r)^2 = 4\pi \cdot 2.25r^2 = 2.25 \cdot (4\pi r^2)
$$

The percentage increase in surface area is calculated as:  
$$
	ext{Percentage Increase} = \frac{	ext{New Surface Area} - 	ext{Original Surface Area}}{	ext{Original Surface Area}} 	imes 100
$$

Substituting the values:  
$$
	ext{Percentage Increase} = \frac{2.25 \cdot (4\pi r^2) - (4\pi r^2)}{4\pi r^2} 	imes 100 = \frac{1.25 \cdot (4\pi r^2)}{4\pi r^2} 	imes 100 = 125\%
$$

Thus, the surface area increases by **125%**.

Answer

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