Question

A storage tank consists of a circular cylinder with a hemisphere stuck on either end. If the external diameter of the cylinder be 1.4 m. and its length be 8 m. find the cost of painting it on the outside at rate of D20 per m2.

Answer 1

Cylindrical part:
length (h) = 8m
diameter = 1.4m
radius (r) = 1.4/2 = 0.7m

Spherical parts at the ends:
radius = 0.7m

Total surface area = CSA of cylinder + 2 × CSA of hemisphere at end

$\Rightarrow TSA = 2\pi rh + 2 \times 2\pi {r}^{2} \\ \\ \Rightarrow TSA =2\pi rh + 4\pi {r}^{2} \\ \\ \Rightarrow TSA =2\pi r(h + 2r) \\ \\ \Rightarrow TSA = 2 \times \frac{22}{7} \times 0.7(8 + 2 \times 0.7) \\ \\ \Rightarrow TSA = 2 \times \frac{22}{7} \times 0.7 \times 9.4 \\ \\ \Rightarrow TSA = 41.36 \: {m}^{2}$

Rate = ₹20 per m^2

Total cost = 41.36 × 20 = ₹827.20

Answer 2

Answer:

Rs 827.20

Step-by-step explanation:

Find the radius:

Radius = Diameter ÷ 2

Radius = 1.4 ÷ 2 = 0.7 m

Find the lateral surface area of the cylinder:

Lateral Surface Area = 2πrh

Lateral Surface Area = 2π(0.7)(8) = 35.2 m²

Find the surface area of the of the two hemispheres:

Note that the two hemispheres will form into a sphere when put together

Surface Area = 4πr²

Surface Area = 4π(0.7)² = 6.16 m²

Find the total surface area:

Total surface area = 35.2 + 6.16 = 41.36 cm²

Find the cost:

1 m² = Rs 20

41.36 m² = 41.36 x 20 = Rs 827.20

Answer: The cost is Rs 827.20