Question

The sum of the base radius and height of a
solid cylinder is 37 cm. If the total surface
area of the solid cylinder is 1628 cm", then
find its height only ​

Answer 1

Step-by-step explanation:

Given r+h=37 cm

Total surface area of the solid cylinder = 2πr(r+h)=1628cm

2

∴r=

2×22×37

1628×7

=7cm

∴ Height = (37-7) cn = 30 cm

and Circumference = 2πr=

7

22

×7=44cm

Volume of the cylinder = πr

2

h=

7

22

×7×7×30=4620cm

3

Answer 2

Given : -

Sum of base radius and height

( R + h ) = 37 cm.  ______(1)

Total surface Area = 1628 cm²

Formula : -

$Total\ surface\ Area = 2\pi R( R + h )$

Solution : -

⇒ $1628 = 2\pi R(R+h)$

⇒ $1628 = 2\pi R(37)$     [ ∵ (R + h) = 37 is given ]

⇒ $R = \frac{1628}{2\pi *37}$

⇒ $R = 7 cm$

From equation (1)

⇒$R+h = 37$

⇒ $h = 37 - 7 = 30 cm$

∴ Height of the cylinder (h) = 30 cm.