Question

The curve surface area and volume of a cylinder is 264 m² and 924 m³ respectively. Find the radius and height?​

Answer 1

Answer:

$radius=7m, Height=6m.$

Step-by-step explanation:

According to the problem,

The curved surface area of the cylinder= 264 $m^{2}$

⇒ $2\pi rh=264$

⇒ $\frac{44}{7} rh=264$

⇒ $rh=264*\frac{7}{44}$

⇒ $rh = 42$

⇒  $h=\frac{42}{r}$

The volume of the cylinder =924 $m^{2}$

⇒ $\pi r^{2}h=924$

⇒ $\frac{22}{7}r^{2}h=924$

⇒ $r^{2}h=924 * \frac{7}{22}$

⇒ $r^{2}h=294$

⇒  $h=\frac{294}{r^{2} }$

By comparing both the value of h we get,

$\frac{42}{r}=\frac{294}{r^{2} }$

⇒ $r=\frac{294}{42}$

⇒ $r=7 m.$

Now we have radius 7 m so by putting the value of same in the surface area formula we get.

⇒ $h= \frac{42}{7}$

⇒ $h=6 m$.