MCQ
The radius of a sphere $($in $cm)$ whose volume is $12 \pi \ cm ^3$ is
- ✓$3^{2 / 3}$
- B$3^{3 / 2}$
- C$3^{1 / 3}$
- D$3^{1 / 2}$
✓
Answer
Correct option: A.
$3^{2 / 3}$
Let radius of the sphere be $r \ cm$.
According to question,
$\frac{4}{3} \pi r^3=12 \pi$
$\Rightarrow r^3=\frac{3 \times 12}{4}=9=3^2 $
$\Rightarrow r=\left(3^2\right)^{1 / 3}=(3)^{2 / 3} \ cm$
According to question,
$\frac{4}{3} \pi r^3=12 \pi$
$\Rightarrow r^3=\frac{3 \times 12}{4}=9=3^2 $
$\Rightarrow r=\left(3^2\right)^{1 / 3}=(3)^{2 / 3} \ cm$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If in two triangles $ABC$ and DEF, $\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{FE}}=\frac{\text{CA}}{\text{FD}},$ then:
→If the sum of the areas of two circles with radii $R1$ and $R2$ is equal to the area of a circle of radius $R$, then:
→The total surface area of solid opened at the top in the given figure is
If $1 / 2$ is a root of the quadratic equation $x^2-m x-5 / 4=0$, then value of $m$ is:
→In the figure, if $PQR$ is the tangent to a circle at $Q$ whose centre is $O$, $AB$ is a chord parallel to $PR$ and $\angle\text{BQR}=70^\circ$ then $\angle\text{AQB}$ is equal to:
→The number of solid spheres, each of diameter 6cm that could be moulded to form a solid metal cylinder of height $45\ cm$ and diameter $4\ cm$, is:
→The area of the triangle formed by the lines $2x + 3y = 12, x - y - 1 = 0$ and $x = 0$.
→The numbers $2,7$ and $k+4$ are in AP then $k=$ ........... .
→The number of decimal places after which the decimal expansion of the rational number $\frac{23}{2^2\times5}$ will terminate, is:
→If $m^{\text {th }}$ term of an A.P. is $1 / n$ and $n^{\text {th }}$ term is $1 / m$, then the sum of first $m n$ terms is
→