Question

Find the height of a cylinder whose volume is 38.5^3and it's diameter of base is 3.5 cm please answer the question with step by step explaination​

Answer 1

Answer:

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Answer 2

$\underline\mathfrak\orange{Given:—}$

A cylinder whose volume is 38.5 m³ and it's diameter is 3.5 cm.

$\underline\mathfrak\orange{To Find :-}$

What is the height of a cylinder.

$\underline\mathfrak\orange{Formula Used :-}$

$\longmapsto \sf\boxed{\bold{\pink{Volume\: Of\: Cylinder =\: {\pi}{r}^{2}h}}}$

.

where,

r = Radius

h = Height

$\underline\mathfrak\orange{Solution :-}$

First, we have to find the radius of a cylinder :

As we know that,

$\longmapsto \sf\boxed{\bold{\pink{Radius =\: \dfrac{Diameter}{2}}}}$

.

$\underline\mathfrak\orange{Given :}$

Diameter = 3.5 cm

According to the question by using the formula we get,

$↦ \sf Radius =\: \dfrac{3.5}{2}$

.

$➦ \sf\bold{\green{Radius =\: 1.75\: cm}}$

Now, we have to find the height of a cylinder :

Let, the height of a cylinder be x cm

.

$\underline\mathfrak\orange{Given :}$

Radius = 1.75 cm

Volume of a cylinder = 38.5 m³

According to the question by using the formula we get,

.

$↦ \sf {\pi}{r}^{2}h =\: 38.5πr$

$↦ \sf \dfrac{22}{7} \times {(1.75)}^{2} \times h =\: \dfrac{385}{10}$

$↦ \sf \dfrac{22}{7} \times 3.06 \times h =\: \dfrac{385}{10}$

$↦ \sf \dfrac{22}{7} \times \dfrac{306}{100} \times h =\: \dfrac{385}{10}$

$↦ \sf h =\: \dfrac{385 \times 7 \times 10\cancel{0}}{1\cancel{0} \times 22 \times 306}$

$↦ \sf h =\: \dfrac{385 \times 7 \times \cancel{10}}{\cancel{22} \times 306}$

$↦ \sf h =\: \dfrac{\cancel{385} \times 7 \times 5}{\cancel{11} \times 306}$

$↦ \sf h =\: \dfrac{35 \times 35}{306}$

$↦ \sf h =\: \dfrac{\cancel{1225}}{\cancel{306}}$

$➠ \sf\bold{\red{h =\: 4.003\: cm(approx)}}$

∴ The height of a cylinder is 4.003 (approx).