Question

A cylindrical well has height 280 m. If cost of digging it is Rs 3,52,000, when rate of digging per cubic metre is Rs 100, find the diameter of the well.

Answer 1

Answer:

$\sf{The \ diameter \ of \ the \ well \ is \ 4 \ m}$

Given:

• A cylindrical well has height 280 m

• The cost of digging it is Rs 3,52,000, when rate of digging per cubic metre is Rs 100.

To find:

$\sf{The \ diameter \ of \ the \ well.}$

Solution:

$\sf{Volume \ of \ well=\dfrac{352000}{100}}$

$\sf{\therefore{Volume \ of \ well=3520 \ m^{3}}}$

$\sf{For \ cylindrical \ well,}$

$\boxed{\sf{Volume \ of \ cylinder=\pi \times \ r^{2}\times \ h}}$

$\sf{\therefore{3520=\pi\times \ r^{2}\times280}}$

$\sf{\therefore{r^{2}=\dfrac{3520\times7}{22\times280}}}$

$\sf{\therefore{r^{2}=\dfrac{32}{2\times4}}}$

$\sf{\therefore{r^{2}=\dfrac{8}{2}}}$

$\sf{\therefore{r^{2}=4}}$

$\sf{On \ taking \ square \ root \ of \ both \ sides}$

$\sf{\longmapsto{r=2 \ m}}$

$\sf{But, \ Diameter=2\times \ r}$

$\sf{\therefore{Diameter=2(2)}}$

$\sf{\therefore{Diameter=4 \ m}}$

$\sf\purple{\tt{\therefore{The \ diameter \ of \ the \ well \ is \ 4 \ m}}}$