Question

The sum of the height and the radius of a solid right circular cylinder is 41cm. If its total surface area is
22
2706cm², then its volume (in cm°) is closest to (Take 1 =
Top 10835
1735931160 35
O 10584
1735931160 3
1735931160 33
O 9568
031160 38
5931160 30
160 35
0 9584
5931160 33​

Answer 1

Correct Question :

The sum of the height and the radius of a solid right circular cylinder is 41cm. If its total surface area is 2706cm², then its volume (in cm³) is.

Given :

• Sum of height and Radius = 41 cm

• Total surface area of the cylinder = 2706 cm².

To find :

The volume of the cylinder .

Solution :

To find the volume of the cylinder , first we should find the radius and the height of the cylinder.

To find the Radius of the Cylinder :

We know the formula for Total surface area of a cylinder i.e,

$\boxed{\bf{TSA = 2\pi r(h + r)}}$

Where :

• TSA = Total surface area
• r = Radius
• h = Height

Now using the above formula and substituting the values in it, we get :

$:\implies \bf{TSA = 2\pi r(h + r)}$

$:\implies \bf{2706 = 2 \times \dfrac{22}{7} \times r \times 41}$

$:\implies \bf{2706 = 2 \times \dfrac{22}{7} \times r \times 41}$

$:\implies \bf{2706 \times 7 = 2 \times 22 \times r \times 41}$

$:\implies \bf{2706 \times 7 = 1804 \times r}$

$:\implies \bf{18942 = 1804 \times r}$

$:\implies \bf{\dfrac{18942}{1804} = r}$

$:\implies \bf{10.5 = r}$

$\boxed{\therefore \bf{r = 10.5\:cm}}$

Hence the radius of the cylinder is 10.5 cm.

To find the height of the cylinder :

According to the givrn , we are provided with the sum of the height and the radius of the cylinder.

And we now know the radius of the cylinder .

According to the Question , our equation is like ;

$\boxed{\bf{h + r = 41}}$

Now using the above equation and substituting the value of r in it, we get :

$:\implies \bf{h + r = 41}$

$:\implies \bf{h + 10.5 = 41}$

$:\implies \bf{h = - 10.5 + 41}$

$:\implies \bf{h = 30.5}$

$\boxed{\therefore \bf{h = 30\:cm}}$

Hence the height of the cylinder is 30 cm.

Volume of the cylinder :

We know the formula for Total surface area of a cylinder i.e,

$\boxed{\bf{V = \pi r^{2}h}}$

Where :

• V = Volume
• r = Radius
• h = Height

Now using the above formula and substituting the values in it, we get :

$:\implies \bf{V = \pi r^{2}h}$

$:\implies \bf{V = \dfrac{22}{7} \times 10.5^{2} \times 41}$

$:\implies \bf{V = 22 \times 15.75 \times 41}$

$:\implies \bf{V = 14206.5}$

$\boxed{\therefore \bf{V = 14206.5\:cm^{3}}}$

Hence the volume of the cylinder is 14206.5 cm³.