Question

find the height of cylinder​

Answer 1

Question :

• A tinmaker converts a cubical metallic box into 10 cylindrical tins. Side of a cube is 50 cm and radius of the cylinder is 7 cm. Find the height of each cylinder so made if the wastage of 12% in incurreal in the process.

Given :

• Side of cube = 50 cm
• Radius of cylinder = 7 cm
• wastage of material = 12 %
• No. of cylinder = 10

To Find :

• Height of the cylinder

Solution :

First we have to find volume of the cube

$\tt Volume_{cube} = {a}^{3} \\ \\ \tt \implies 50 \times 50 \times 50 \\ \\\tt \implies 125000 \: {cm}^{3} \\ \\ \tt volume \: of \: cube \: is \: 125000 \: {cm}^{3}$

12 % tin has wasted in making of cylinder

$\tt 12\% \: of \: 125000 \\ \\ \tt \implies \frac{12}{ \cancel{100}} \times 1250 \cancel{00} \\ \\ \tt \implies15000 \\ \\ \tt materia \: \: left \: \: for \: \: cylinder\\ \\ \tt 125000 - 15000 = 110000 {cm}^{3}$

Now We have Volume and radius of Cylinder by which we can find height of Cylinder

$\tt vol \: of \: 10 \: cylinder = 110000 \\ \\ \tt vol \: of \: 1 \: cylinder = \frac{110000}{10} = 11000 {cm}^{3}$

By Volume of the cylinder :

$\tt Volume_{cylinder} = \pi {r}^{2}h \\ \\ 11000 = \frac{22}{7} \times 7 \times 7 \times h \\ \\\tt h = \frac{11000}{22 \times 7} \\ \\ \tt h ≈ 71.46\:cm \\ \\ \large \underline{\tt \blue{Height \: of \: cylinder \: is \: 71.46\: cm}}$