Question

the radius and height of a cylinder are in the ratio 4 is to 7 and its volume is 2816 cM cube find its total surface area

Answer 1

$\huge\bold\red{Solution : \longrightarrow}$

Radius:Height of the cylinder = 4:7

Let Radius be 4x cm and Height be 7x cm.

Volume of the cylinder = 2816 cm³

$\mathfrak{ = > \pi {r}^{2} h = 2816}$

$\mathsf{ = > \frac{22}{7} \times 4x \times 4x \times 7x = 2816}$

$\mathsf{ = > 352 {x}^{3} = 2816}$

$\mathsf{= > {x}^{3} = \frac{2816}{352}}$

$\mathsf{= > {x}^{3} = 8}$

$\mathsf{ = > x = \sqrt[3]{8}} \\ \\ \mathsf{= > x = 2}$

•°• Radius = 4x = 4 × 2 = 8cm

And Height = 7x = 7 × 2 = 14cm

•°• TSA of the cylinder

$\mathfrak{ = 2\pi {r}^{} (h + r)}$

$\mathfrak{ = [2 \times \frac{22}{7} \times 8 \: \: (14 + 8) ]\: {cm}^{2} }$

$\mathfrak{ = ( \frac{352}{7} \times 22) \: {cm}^{2}} \\ \\ \mathfrak{= 1106.28 \: \: {cm}^{2}}$

$<marquee>I HOPE IT WILL HELP YOU<marquee>$

Answer 2

Solution:
Let radius (r) =4x
height(h)=7x

Volume (V) = 2816 cm 3
We have ,
V = pie *r^2 *h
$v = \pi \times r {}^{2} \times h$

or, 2816 cm3 = (22/7) *(4x)^2*7x
or, 2816 cm3 = 352 x3
or, x3 = 2816 cm3 / 352
or, x3=8
$\sqrt{8} = 2$
Now,
r= 8 cm
h=14 cm

Hence, T.S.A=
$2 \times \pi \times r \times (r + h )$
=2x(22/7)x8x(8+14)


=1106.28 (ans)*




*Not sure for the solution!!!!!!