Question

14/ If the radius of a sphere is doubled, how many times will its (a) surface area, (b) volume
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Answer 1

FORMULA

The volume of a sphere is=(4/3)πr^3

IF THE RADIUS OF THE SPHERES ARE r and R RESPECTIVELY .....

AND IF THE CORRESPONDING VOLUMES AND. AREAS ARE =v and V ; a and A.

then.....

$\frac{v}{V} = ( \frac{r}{R} ) {}^{3} \\ and \\ \frac{a}{A} =( \frac{r}{R} ) {}^{2}$

SOLVING

now radius is doubled....R=2r

volume

$\frac{v}{V} = (\frac{r}{2r} ) {}^{3} =( \frac{1}{2} ) {}^{3} = \frac{1}{8} \\ = 1:8$

area

$\frac{a}{A} = (\frac{r}{2r} ) {}^{2} \\ =( \frac{1}{2} ) {}^{2} \\ = \frac{1}{4} \\ = 1:4$

ANSWERS

• The volume will be increased by 8 times
• The area will be increased by 4 times