Question

solve the question.......​

Answer 1

Answer :

1. The radius of the cylindrical pipe is 7 units.
2. The height of the cylindrical pipe is 20 units.

Step-by-step explanation:

Given :

The top circled area of the cylinder = 154 sq. units.

The curved Surface Area of the cylinder = 880 sq. units.

To Find :

The radius and the height of the cylindrical pipe.

Solution :

Top circled area = 154 sq. units.

So,

$\sf\\ \\ \implies \pi \: {r}^{2}= 154 \\ \\ \implies \dfrac{22}{7} \times {r}^{2} = 154 \\ \\ \implies {r}^{2} = 154 \times \dfrac{7}{22}\\ \\ \implies \dfrac{154}{22} = 7 \\ \\ \implies {r }^{2} = 7 \times 7 \\ \\ \implies {r}^{2} = 49 \\ \\ \implies r = \sqrt{49} \\ \\ \implies r = 7$

∴ The radius of the cylindrical pipe is 7 units.

$\rule{300}{1.4}$

Curved Surface Area = 880 sq. units

So,

$\sf\\ \implies 2\pi \: rh = 880\\ \\ \implies 2 \times \dfrac{22}{7}\times 7 \times h = 880\\ \\ \implies 44 \times h = 880\\ \\ \implies h = \dfrac{880}{44}\\ \\ \implies h = 20$

∴ The height of the cylindrical pipe is 20 units.

Answer 2

$\bold{\Huge{\underline{\boxed{\rm{\red{ANSWER\::}}}}}}$

Given:

In a figure a cylindrical pipe the area of the surface are given.

$\bold{\Large{\underline{\sf{\pink{To\:find\::}}}}}$

The radius and height of the cylinder.

$\bold{\Large{\underline{\sf{\purple{Explanation\::}}}}}$

We have,

• Area of circle= 154 sq.units
• Curved surface area of cylinder= 880 sq.units

According to the question:

• Area of circle:

We know that formula of the area of circle: πr²  [sq.units]

→ πr² = 154

→ $\bold{\frac{22}{7} *r^{2} =154}$

→ r² = $\bold{\frac{\cancel{154}*7}{\cancel{22}} }$

→ r² = (7×7) sq.units

→ r² = 49 sq.units

→ r = √49 sq.units

→ r = 7cm

Now,

• Curved Surface area of cylinder:

We know that formula of the C.S.A: 2πrh   [sq.units]

→ 2πrh = 880

[putting the value of r in above formula]

→ $(\bold{2*\frac{22}{7} *7*h=880)sq.units}$

→ $(\bold{\frac{44}{\cancel{7}} *\cancel{7}*h=880)sq.units}$

→ 44h = 880

→ h = $\bold{\cancel{\frac{880}{44}} }$

→ h = 20cm

Thus,

The radius of the cylinder is 7cm & height is 20cm.