Question

find the volume of a sphere whose radius a)16
​

Answer 1

$\large{\underline{\underline{\frak{\;Understanding\; the\; Question\;:}}}}$

• Here, the concept of Surface area and volume has been used. Here, we're given with the radius of a sphere. We've been asked to calculate the volume of sphere. The question is quite simple we just need to know the formula. So, after examining the formula, just equate the value of radius in it.

$\large{\underline{\underline{\frak{\; Formula\; Used\;:}}}}$

» Here, we've to calculate the volume of sphere. Volume of sphere is the product of four third, pi and cube of radius of sphere. The formula of volume of sphere is given by:

$\qquad\qquad\star~{\underline{\boxed{\pmb{\frak{Volume\; of\; sphere=\dfrac{4}{3}\times \pi\times {r}^{3}}}}}}$

where:

• π is pi, the mathematical constant that is 22/7.
• r is the radius of the sphere.

$\begin{gathered}\rule{230px}{.2ex}\\\end{gathered}$

$\large{\underline{\underline{\frak{\; Solution\;:}}}}$

It is stated in the question that the radius of the sphere is 16 units. We know, the formula for volume of sphere. So,

$:\implies\quad\sf{Volume\; of\; sphere=\dfrac{4}{3}\times \pi\times {r}^{3}}$

Now, let's equate the value of pi and radius in essence, 22/7 and 16 respectively.

$:\implies\quad\sf{Volume\; of\; sphere=\dfrac{4}{3}\times\dfrac{22}{7}\times {16}^{3}}$

Let's perform multiplication between fractions. Multiplying numerators and denominators of fractions.

$:\implies\quad\sf{Volume\; of\; sphere=\dfrac{88}{21}\times 4096}$

Now, let's convert the fraction into decimal form for further calculation.

$:\implies\quad\sf{Volume\; of\; sphere=4.1904\times 4096}$

Now, performing multiplication. $\\:\implies\quad\underline{\boxed{\pmb{\frak{Volume\; of\; sphere\approx \red{17,163.8784\; units}}}}}$

Required answer:

❝Henceforth, the volume of sphere is 17,163.8784 units approx..❞

$\begin{gathered}\rule{230px}{.2ex}\\\end{gathered}$

$\qquad\qquad\boxed{\boxed{\purple{\sf{\;\;More\; to\; know\;\;}}}}$

• Volume of cuboid = lbh
• Volume of cube = a³
• Volume of cylinder = πr²h
• Volume of cone = 1/3 πr²h
• TSA of cuboid = 2(lb+bh+hl)
• TSA of cube = 6a²
• TSA of cylinder = 2πr(r+h)
• TSA of cone = πr(r+l)
• TSA of sphere = 4πr²