Question

the capacity of a cylindrical jar is 550 litres of water . If the height of the jar is 28 decimetre , what is it's diameter​

Answer 1

Given :-

• Capacity of cylindrical jar = 550 litres

• Height of cylindrical jar = 28 dm

To Find :-

• Diameter of cylindrical jar.

Formula Used :-

$\purple{\boxed{ \bf \:Volume_{(Cylinder)} = \pi \: {r}^{2}h}}$

$\purple{\boxed{ \bf \:1 \: litre \: = \: 1 \: {dm}^{3}}}$

$\purple{\boxed{ \bf \:diameter \: = \: 2 \times radius}}$

Solution :-

Given that

$\rm :\longmapsto\:Volume_{(Cylindrical \: jar)} = 550 \: litres = 550 \: {dm}^{3}$

$\rm :\longmapsto\:Height_{(Cylindrical \: jar)}, \: h \: = \: 28 \: dm$

Let radius of cylindrical jar = 'r' dm

Now,

Using,

$\rm :\longmapsto\:Volume_{(Cylindrical \: jar)} = \pi \: {r}^{2}h$

$\rm :\longmapsto\: \red{\cancel{550}} \: \: ^{25} = \dfrac{ \red{ \cancel{22}}}{ \cancel7} \times {r}^{2} \times \cancel{28} \: \: ^{4}$

$\rm :\longmapsto\: {r}^{2} = \dfrac{25}{4}$

$\rm :\implies\:r = \dfrac{5}{2} \: dm$

So,

$\bf :\longmapsto\:Diameter_{(Cylindrical \: jar)}, \: d \: = \: 2r \: = 5 \: dm$

Additional Information :-

$\boxed{ \sf{ \: TSA{(cone)} = {6(edge)}^{2} }}$

$\boxed{ \sf{ \: TSA{(cuboid)} = 2(lb + bh + hl)}}$

$\boxed{ \sf{ \: TSA{(cone)} = \pi \: r(l + r)}}$

$\boxed{ \sf{ \: TSA{(cylinder)} = 2\pi \: r(h + r)}}$

$\boxed{ \sf{ \: CSA{(cube)} = 4 \times {(edge)}^{2} }}$

$\boxed{ \sf{ \: CSA{(cone)} = \pi \: rl}}$

$\boxed{ \sf{ \: CSA{(cuboid)} = 2(l + b) \times h}}$

$\boxed{ \sf{ \: CSA{(cylinder)} = 2\pi \: rh}}$

$\boxed{ \sf{ \: Volume_{(cube)} = {(edge)}^{3} }}$

$\boxed{ \sf{ \: Volume_{(cuboid)} = lbh}}$

$\boxed{ \sf{ \: Volume_{(cone)} = \dfrac{1}{3} \pi \: {r}^{2} h}}$

$\boxed{ \sf{ \: Volume_{(sphere)} = \dfrac{4}{3} \pi \: {r}^{3} }}$