Question

Find the diameter of a 10 inch long cylindrical bottle whose volume is 196.25 cubic inches.
{Hint : volume = (3.14)(radius)^2(height)

Answer 1

${\large{\bold{Given:}}}$

• Height = 10 inch
• Volume = 196.25 inch³

${\large{\bold{To \ Find:}}}$

• What is the diameter of cylinder ?

${\large{\bold{Formulas \ Used :}}}$

${\ddag \: \: {\small{\sf{\boxed{\blue{Volume_{(Cylinder)} = \pi r^2 h}}}}}}$

${\large{\bold{Solution:}}}$

${\small{\tt{Volume_{(Cylinder)} = 196.25 inch^3}}}$

${\longmapsto \: {\small{\tt{\pi r^2 h = 196.25 \: inch^3}}}}$

${\longmapsto{\small{\tt{ 3.14 × r^2 × 10\ inch = 196.25\ inch^3 }}}}$

${\longmapsto{\small{\tt{ r^2 = \dfrac{ 19625\ inch^3 × 100}{314 × 100× 10 \ inch}}}}}$

${\longmapsto{\small{\tt{r^2 = \dfrac{1962.5 \ inch^2}{314}}}}}$

${\longmapsto{\small{\tt{r^2 = 6.25 \ inch^2}}}}$

${\longmapsto{\small{\tt{ r = \sqrt{6.25 \ inch^2}}}}}$

${\longmapsto{\small{\tt{ r = 2.5 \ inch }}}}$

We know that ,

${\leadsto{\small{\tt{ Diameter = 2 × Radius}}}}$

${\leadsto{\small{\tt{ Diameter = 2 × 2.5 \ inch}}}}$

${\leadsto{\small{\tt{ Diameter = 5 \ inch}}}}$

${\red{\leadsto{\underline{\boxed{\frak{\small{ \therefore Diameter \ of \ cylinder = 5 \ inch}}}}}}}$