Question

19. A mathematics teacher took her grade X students to the Taj Mahal. It was an educational trip. She was interested in history also. On reaching there she told them about the history and facts about the seventh wonder. She also told them that the structure of the monument is a combination of several solid figures. There are 4 pillars that are cylindrical in shape. A big dome in the center and 2 more small domes on both sides of the big dome on its side. The domes are hemispherical. The pillars also have domes on them

I. How much cloth material will be required to cover a big dome of a diameter of 7m? a. 77 m b. 78 m c. 79 m? d. 80 m ii. Write the formula to calculate the volume of the pillar

a. ar h + ar b.ar h + ) or l c. arl + ar d. r h + ii. How much is the volume of the hemisphere if the radius of the base is 3 m? a. 65.57 m b. 75.77 m c. 56.57 m d. 85.57 m iv. Find the curved surface area of 4 pillars if the height of pillars is 7.5 m and the radius

of the base is 2.5 m. a. 768.56 m b. 658.56 m c. 766.56 m? d. 628.57 m

v. What is the ratio of the sum of volumes of two-cylinder of radius 1 cm and height 2cm each to the volume of a sphere of radius 3 cm?​

Answer 1

(i) How much cloth material will be required to cover a big dome of a diameter of 7m ?

a. 77 m b. 78 m c. 79 m? d. 80 m

Answer :-

→ CSA of dome in the shape of hemisphere = 2πr² = 2 * 22/7 * (7/2)² = (2 * 22 * 7) / 4 = 11 * 7 = 77 m² (a)

(ii) Write the formula to calculate the volume of the pillar ?

a. ar h + ar b.ar h + ) or l c. arl + ar d. r h +

Answer :-

→ Volume of Pillar in the shape of cylinder = πr²h .

(iii) How much is the volume of the hemisphere if the radius of the base is 3 m ?

a. 65.57 m b. 75.77 m c. 56.57 m d. 85.57 m

Answer :-

→ Volume of hemisphere = (2/3)πr³ = (2/3) * 3.14 * (3)³ = 2 * 3.14 * 9 = 56.57 m³ (c) .

(iv) Find the curved surface area of 4 pillars if the height of pillars is 7.5 m and the radius of the base is 2.5 m.

a. 768.56 m b. 658.56 m c. 766.56 m? d. 628.57 m

Answer :-

→ CSA of 4 pillars = 4 * 2πrh = 8πrh = 8 * 3.14 * 2.5 * 7.5 = 471 m².

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