Question

A cylinder vessel open at the top has a base diameter 56 CM if the total cost of painting the outer curved surface of the vessel is Rs 352 at the rate of Rs 0.2 per 100 cm square then what is the height of the vessel of?

Answer 1

Answer:

The height of the vessels is 1000 cm

Explanation:

Since, we know that

Curved Surface Area of a cylinder =$2\pi rh$ where r is the radius and h is the height of the cylinder

Given:

Diameter(d) = 56 cm

radius(r) = $\frac{d}{2}$ = $\frac{56}{2}=28$ cm

cost of painting = Rs 0.002 [ as rate is Rs 0.2 per 100 cm square]

Total cost of painting= Rs. 352

then,

total cost of painting = outer curved surface area of vessel x Cost of painting

therefore, we have,

$2\pi rh \times 0.002 =352$  where $[\pi =\frac{22}{7} ]$

⇒$2\times \frac{22}{7} \times 28 \times h \times 0.002 =352$

Simplify:

$44\times 4 \times h\times 0.002 =352$

⇒  $176 \times 0.002 \times h= 352$

⇒ $h=\frac{352}{176 \cdot 0.002}$

On simplify we get,

h= 1000 cm.

Answer 2

Answer-

The height of the vessel is 10m.

Solution-

The diameter of the cylindrical vessel = 56 cm, let us assume the height is h cm

Curved surface area of the cylinder is,  

$\Rightarrow A=\pi \times d\times h$

Putting the values,

$\Rightarrow A=\pi \times 56\times h$

$\Rightarrow A=175.93h$

If the total cost of painting the outer curved surface of the vessel is 352 rupees at the rate of 0.2 per 100 cm²

i.e 0.2 rupees is spent for painting 100 cm², so calculation for 252 will be give us the area.

Area of the curved surface will be

$=\frac{100\times 352}{0.2} =176,000\ cm^2$

This two expressions of the area will be the same because they are the same cylinder,

$\Rightarrow 175.93h=176,000$

$\Rightarrow h=\frac{176,000}{175.93}=1000.39\approx 1000\ cm$

$\Rightarrow h=10\ m$

Therefore, the height of the vessel is 10m