Question

The inner diameter of a cylindrical vessel is 3.5 cm. It is 100m deep. Find the cost of polishing the inner curved surface area at the rate of ₹20 per m2 find the the radius of the base​

Answer 1

Step-by-step explanation:

The lateral or curved surface area of a right circular cylinder is equal to the product of the circumference of a base by the altitude or depth:

S = 2.π.r.h ………………………………………………………… ………(1)

where, r=radius of base, h=altitude

Total cost of painting the curved area=Rs2200

Cost of painting = Rs20 per square meter

∴ Area of the curved surface (S)

= Total cost of painting/cost of painting

= 2200/20

= 110 square metre

Given depth (altitude) of the vessel h = 10 meter

Substituting for S = 110 and h = 10 in (1),

110 = 2.π.r.10

Or, r = 110/(2.π.10) =11/(2.π) = 5.5/π (Dividing both sides by 2.π.10 and simplifying}

Now for π we will use Aryabhata’s value of 3.1416 which is correct to 4 decimal places. This gives

r = 5.5/3.1416 = 1.7507 meters

∴ Radius of the base of the cylinder = 1.7507 meters (Answer)

Answer 2

GIVEN :—

→ Inner diameter of a cylindrical vessel = 3.5 m.

→ Height of a cylindrical vessel= 100 m.

TO FIND :—

→ The cost of polishing the inner curved surface area (CSA) at the rate of ₹ 4 per m².

SOLUTION :—

→ To find the cost = ?

The inner diameter of a cylindrical vessel = 3.5 m.

So radius =$\sf \dfrac {3.5}{2} \ = \ 1.75 \ {m}^{2}$

Inner curved surface area (CSA) = $\sf 2 \pi rh$

Put the values given values.

$\implies \sf 2 \times \dfrac {22}{7} \times 1.75 \times 1.75 \times 100$

$\implies \sf 1925 m^{2}$

Total cost of polishing = 1925 × 4

∴ Total cost of polishing is ₹ 7700.