Question

find the lateral area and surface area of a cylinder with a base area of 49π and a height that is 2 times the radius​

Answer 1

Given

• Base area of Cylinder= 49π
• Height = 2 radius

To Find

• lateral area and surface area of a cylinder

Formula used

$\boxed{\bf{Lateral\ area \ of\ Cylinder= 2πrh}}$

$\boxed{\bf{Surface\ Area \ of\ Cylinder= 2πr(r+h)}}$

Solution

• To Find The lateral and Surface area of Cylinder we need to Find the Radius and Height Of Cylinder.And it is Given That Base area of Cylinder is 49π . So from the Base area we will find Height and radius . After finding the Radius and Height we will Find Lateral and Surface area.

$\sf{Base\ area\ of \: Cylinder = 49π}$

$\dashrightarrowπ {r}^{2} = 49π$

$\dashrightarrow{r}^{} = \sqrt{49}$

$\dashrightarrow{r}^{} = 7 \:$

• It is Given That the Height is 2 time's the Radius

So,

Height= 7×2= 14

Now

• Height of Cylinder= 14
• Radius of Cylinder=7

$\boxed{\bf{Lateral\ area \ of\ Cylinder= 2πrh}}$

$\sf{Lateral\ area \ of\ Cylinder= 2 \times \cfrac{22}{7} \times 7 \times 14 }$

$\sf{Lateral\ area \ of\ Cylinder= {44} \times 14 }$

$\sf{Lateral\ area \ of\ Cylinder= 616 }$

Now

$\boxed{\bf{Surface\ Area \ of\ Cylinder= 2πr(r+h)}}$

$\sf{Surface\ Area \ of\ Cylinder= 2 \times \cfrac{22}{7} \times 7 \times (7+14)}$

$\sf{Surface\ Area \ of\ Cylinder= 44\times 21}$

$\sf{Surface\ Area \ of\ Cylinder= 44\times 21}$

$\sf{Surface\ Area \ of\ Cylinder= 924}$

Hance,

• Lateral area of Cylinder= 616
• Surface area of Cylinder= 924

Figure of Cylinder:

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