Question

The sum of the height and the radius of the base of a cylinder is 34cm. if the total surface area of the cylinder is 2,992cm square, find the radius.

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Answer 1

Given:-

Total Surface Area of cylinder = 2992 cm²

To find:-

Radius of the base of cylinder.

Assumption:-

Let the height of the cylinder be h

Let the radius of base of the cylinder be r

Solution:-

ATQ,

Sum of radius of base and height of cylinder = 34 cm

Therefore,

$\sf{r + h = 34\:cm \longrightarrow (i)}$

We know,

$\sf{Total\:Surface\:Area\:of\:Cylinder = 2\pi r(r+h) \:sq.units}$

Hence,

$\sf{2992 = 2\pi r(r+h)}$

= $\sf{2992 = 2\times \dfrac{22}{7}\times r\times 34\:\:\:[\because r+h = 34\:From\:eq.(i)}$

$\sf{\implies \dfrac{2992 \times 7}{2\times 22} = 34r}$

$\sf{\implies r = \dfrac{2992\times7}{2\times22\times34}}$

$\sf{\implies r = 14\:cm}$

$\sf{\therefore The\:radius\:of\:the\:base\:of\:cylinder\:is\:14\:cm}$

Some Formulas:-

• $\sf{CSA \:of\:cylinder = (2\pi rh)\:sq.units}$

• $\sf{TSA\:of\:cylinder = 2\pi r(r+h)\:\:sq.units}$

• $\sf{Volume\:of\:cylinder = (\pi r^h)\:\:cubic\:units}$

Note:-

• TSA = Total Surface Area
• CSA = Curved Surface Area

Answer 2

Given

• Sum of height and radius of the base of a cylinder is 34cm.
• Total surface area of the cylinder is 2,992cm².

To find

• Radius of the base.

Solution

• Let the radius of the base be x.
• Let the height of the cylinder be y.

$\therefore$ r + h = 34

We know that

$\underline{\boxed{Total\: surface\: area\: of\: a\: cylinder = 2πr(r + h)}}$

→ 2992 = 2 × 22/7 × r × 34 $\because[{(r+h) = 34}]$

→ 2992 = 44/7 × 34r

→ 34r = (2992 × 7)/44

→ 34r = 20944/44

→ 34r = 476

→ r = 476/34

→ r = 14

Hence, radius of the base is 14cm.

$\rule{200}3$