Bissoy.com
Doctors Medicines MCQs Q&A

A hemispherical dome is open from its base and is made of iron. Thickness of dome is 3.5 meter. Total cost of painting domes outer curved surface is Rs. 2464. If the rate of painting is Rs. 8 per meter2, then what is the volume (in meter3) of iron used in making dome?

A hemispherical dome is open from its base and is made of iron. Thickness of dome is 3.5 meter. Total cost of painting domes outer curved surface is Rs. 2464. If the rate of painting is Rs. 8 per meter2, then what is the volume (in meter3) of iron used in making dome? Correct Answer 628.83

Outer curved surface area = Cost of painting the surface / Rate of painting

⇒ 2464/8 = 308 m2

Outer curved surface area = 2πRo2

308 = 2 × 22/7 × Ro2

(308 × 7) / (2 × 22) = Ro2

49 = Ro2

Ro = 7 m

Ri = Ro - thickness = 7 - 3.5 = 3.5 m

Volume of the hemispherical dome = 2/3 π (Ro3 - Ri3)

⇒ 2/3 × 22/7 × (73 - 3.53) = 628.83 m3

Related Questions

A hemispherical dome is open from its base and is made of iron. Thickness of dome is 3.5 meter. Total cost of painting domes outer curved surface is Rs 2464. If the rate of painting is Rs 8 per meter2, then what is the volume (in meter3) of iron used in making dome?
If the ratio of per-unit cost of painting the curved surface to the per-unit cost of painting the plane surface of a cylinder is 3: 2 while the ratio of the total cost of painting the curved surface to that of both the plane surfaces is 9: 8, then the height of the cylinder is what percent of its radius?
Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relation among the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. The options represent the relations among three quantities. A. < B. > C. ≤ D. ≥ E. = Quantity 1: There is a square field of side 4 meter. A flower bed is to be prepared in its centre, leaving a gravelled path of uniform length around the flowerbed. The cost of preparing the flowerbed and gravelling the path is Rs. 100 and Rs. 200 per square meter respectively. If the total cost is Rs. 1756 then find the double of  width of gravelled path. Quantity 2: The height of a cone is 45 cm. A small cone is cut from it parallel to the base. If the ratio of volume of small cone and the remaining part is 8 : 19 then what is the height from the base from where the cone was cut? Quantity 3: A cylindrical container of radius 60 cm and height 150 cm is filled with ice cream. 10 cones of equal volume need to be prepared from the whole ice-cream. These cones has hemispherical top and the height of the conical portion is 4 times the radius of hemisphere. Find radius of the hemisphere. 
Which of the following statements is/are true? A: If radius of a cylinder is decreased by 50% and its volume remains same, then its height will be increased by 200%. B: Difference between the curved surface area and total surface area of a cone is equal to the area of its circular base. C: If height of a cylinder is equal to its radius, then its curved surface area will be equal to the total area of its both the circular bases.
A metallic hemispherical bowl is made up of steel. The total steel used in making the bowl is 342π cm3. The bowl can hold 144π cm3 water. What is the thickness (in cm) of bowl and the curved surface area (in cm2) of outer side?
‘Grand Slam’ refers to winning certain major tennis tournaments in a single calendar year. The name of the tournaments are A. Australian Open, French Open and US Open B. Australian Open, French Open, Wimbledon and US Open.  C. French Open, US Open and Wimbledon D. French Open, US Open, Wimbledon and Olympic
If the cost of painting the surface of the cone is Rs. 5/m2 and cost of painting the flat surface is Rs.550 less than that of painting the curved surface. If the height of the cone is √95 cm, then what will be the slant height of the cone?
Curved surface area of cone is to be painted. Volume and height of cone is 15400 cm3 and height 12 cm. If painting cost is at rate of Rs. 15 per cm, then what will be the total painting cost?
A square room has a square carpet symmetrically placed in it. This leaves an uncovered area of 9 meter2. The area of the whole romm is 25 meter2 . What is the length of the one side the carpet?
A cylindrical Toy, whose base diameter is 10 cm. The cost to cover its curved surface area at the rate of Rs. 0.2 sq cm is Rs. 330. Now a cone having same base diameter as cylinder is mounted on cylinder. If total height of the Toy is 64.5 cm.  Find the total curved surface area of the Toy?