Question

The volume of a greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is

Answer 1

Answer:

Volume of greatest sphere implies the sphere has the largest radius possible.

According to the question, the radius of the cylindrical log is 1 cm.

Therefore the maximum possible radius of the sphere is 1 cm.

We know that,

$\text{Volume of Cylinder is} \: \dfrac{4}{3} \pi r^3$

Therefore substituting the radius as 1 cm we get,

$\rightarrow \text{Volume of Sphere} = \dfrac{4}{3} \times 3.14 \times 1 \\\\\rightarrow \text{Volume of Sphere} = 4.186\: cm^3$

Hence the volume of greatest sphere that can be cut from a cylindrical log of radius 1 cm is 4.186 cm³

Answer 2

Answer:

$\huge{\boxed{\mathfrak\blue{Answer\::4.189{cm}^{3}(Approx.)}}}$

Solution:-

The radius of the cylindrical log is 1 cm and height is 5 cm.

Volume of the greatest sphere will be cut of from the cylindrical log. As the radius of the cylindrical log is 1 cm , so the maximum value of radius of the greatest sphere will be 1 cm.

Formula used:-

Volume if cylinder = $\frac{4}{3} \pi{r}^{3}$

$\Rightarrow\tt Volume\:of\:cylinder =\frac{4}{3}\pi\times {1}^{3} \\ \\ \Rightarrow\tt Volume\:of\:cylinder=\frac{4}{3} \times 3.1416 \times 1 \\ \\ \Rightarrow\tt Volume\:of\:cylinder = 4.189 {cm}^{3}$

$\therefore\tt {\underline{Volume\:of\:cylinder=4.189{cm}^{3}(Approx.)}}$