The surface area of a sphere is..m

Question

The surface area of a sphere is $102\ \mathrm{cm}^{2}$. If the sphere is cut into two hemispheres, what will be the change in surface area ?.

My attempt;

$$ \mbox{Surface area of sphere}\ = 102\,,\quad4\pi r^2=102\,,\quad r=2.8484\ \mathrm{cm} $$

If the sphere is cut into two hemispheres l,

Surface area of hemisphere $=2\pi r^{2} = 50.9984\ \mathrm{cm}^{2}$.

I have calculated till here. But I did not understand what the question is asking ?.

Note that both "new" surfaces have "bases" with surface area equal to $\pi r^2$. — Mark Viola, Nov 08 '16 at 16:42
$4\pi r^2 +\pi r^2+\pi r^2=6\pi r^2=\frac32 \times ,,\text{surface area of the sphere}$ — Mark Viola, Nov 08 '16 at 16:46
Cut an apple in matching halves. Can you see that there is a "flat" part on each half? — Mark Viola, Nov 08 '16 at 16:48
What is the surface area of the flat part of one of the halves? — Mark Viola, Nov 08 '16 at 16:51
Yes, it is. And you have two halves. The original part of the surface is still there (so that is $4\pi r^2$) and by cutting, we introduce two new portions of surface area each with $\pi r^2$. The total is then $6\pi r^2$. — Mark Viola, Nov 08 '16 at 16:55

score 2 · Accepted Answer · answered Nov 08 '16 at 17:01

Upon cutting the sphere into hemispheres, each hemisphere has original surface area $2\pi r^2$ plus the new "flat" part with surface area $\pi r^2$.

Thus, the new total surface area $S_{new}$, is, therefore, $S_{new}=6\pi r^2 =\frac32 \times \,\,\text{Surface Area of the Sphere}=153\,\,\text{cm}^2$. The change in surface area is thus $51\,\,\text{cm}^2$.

The surface area of a sphere is..m

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