Question

The sum of tyhe base radius and height of a solid cylinder is 37cm. If the total surface area of the solid cylinder is 1628cm find its height

Answer 1

Answer : 30 cm

Step by step explanation :

Lets assume that r and h are the radius and height of the solid cylinder respectively.

Given that :

r + h = 37 cm

Total surface area of the cylinder = 1628 cm2

∴ 2 π r (r + h) = 1628 cm2

=> 2 π r × 37 cm = 1628 cm2

=> 2 × 22/7 × r × 37 = 1628

=> (1628 × 7) / (2 × 22 × 37) = r

=> r = 7 cm

Now,

r + h = 37 cm ( Given )

∴ 7 + h = 37 cm

=> h = 37 – 7 = 30 cm

Hence,

Height of the solid cylinder is 30 cm.

Answer 2

Answer :

The height of the cylinder is 30 cm.

Step-by-step explanation :

Let the radius of the cylinder be $r$ cm.

Then height will be $h$ cm.

Given, $(r+h)=37$ cm.

Total surface area = $1628\:cm^2$

➡️ $\large{1628=2\pi r(r+h)}$

➡️ $\large{1628=2\times\frac{22}{7}\times r(37)}$

➡️ $\large{r=\frac{(1628\times 7)}{(2\times 22\times 37)}}$

➡️ $\large{r=7}$ cm

Since, $(r+7)=37$ cm

Therefore, $h=30$ cm