Question

2. The rest of painting total outside surface of a closed cylindrical box at er 10 cm cube is Rs 1540. The height of the tank
is equal to its radius. Find the volume of cylinderical tank.​

Answer 1

Correct Question:

The cost of painting total outside surface of a closed cylindrical box at per 10 cm square is Rs 1540. The height of the tank is equal to its radius. Find the volume of cylinderical tank$.$

Required Answer:-

Given:

• Height = radius (let x)
• Cost of painting/10 cm³ = Rs. 1540

To FinD:

• Volume of the cylindrical tank?

Solution:

As per the question,

➛Total surface area × Rs. 10/cm² = Rs. 1540

➛Total surface area = Rs. 1540 / Rs. 10/cm²

➛Total surface area = 154 cm²

Now, we know the formula

➛2πr(h + r) = 154 cm² (given)

➛2πx(2x) = 154 cm²

➛2 × 22/7 × 2x² = 154 cm²

➛88/7 × x² = 154 cm²

➛x² = 154 × 7/44 cm²

➛x² = 7 × 7/4 cm²

➛x² = 49/4 cm²

➛x = 7/2 cm

That is approx. 3.5 cm

Finding volume:

= πr²h

= 22/7 × 7/2 × 7/2 × 7/2 cm³

= 134.75 cm³

Hence:-

• The volume of the cylindrical tank is 134.75 cm³

Answer 2

Answer:

Correct Question :-

The cost of painting total outside surface of a closed cylindrical box at per 10 cm square is Rs 1540. The height of the tank is equal to its radius. Find the volume of cylinderical tank..

Given :-

• Height = Radius
• Cost of painting/10 cm = Rs. 1540

To Find :-

Volume

Solution :-

Let the radius be r

TSA × 10 = ₹1540

TSA = 1540/10

TSA = 154 m

Now,

Finding r

2πr(h + r) = 154 cm²

2πr(2r) = 154 cm²

2 × 22/7 × 2r²= 154 cm²

88/7 × r² × 154 cm²

r² = 154 × 7/44 cm²

r² = 7 × 7/4 cm²

r² = 49/4 cm²

r² = √49/4

r = 7/2 cm

r = 3.5 cm

Now,

Volume = πr²h

22/7 × 7/2 × 7/2 × 7/2

22 × 1/2 × 7/2 × 7/2

11 × 1 × 7/2 × 7/2

134.75 cm³

Therefore :-

Volume of Cylinder is 134.75 cm³