Mathematics teacher of a school took her 9th standard students to show Gol Gumbaz. It was a part of their Educational trip. The teacher had interest in history as well. She narrated the facts of Gol Gumbaz to students. Gol Gumbaz is the tomb of king Muhammad Adil Shah, Adil Shah Dynasty. Construction of the tomb, located in Vijayapura , Karnataka, India, was started in 1626 and completed in 1656. It reaches up to 51 meters in height while the giant dome has an external diameter of 44 meters, making it one of the largest domes ever built. At each of the four corners of the cube is a dome shaped octagonal tower seven stories high with a staircase inside
(a) What is the curved surface area of hemispherical dome ?
(i) 908m2
(ii) 968 m2
(iii) 340 m2
(iv) 780 m2
(b) What is the height of the cuboidal part ?
(i) 14 m (ii) 7 m (iii) 29 m (iv) 18 m
(c) What is the circumference of the base of the dome ?
(i) 34 ii) 22 iii) 44 iv) 55
(d) The total surface area of hemispherical dome having radius 7cm including base
(i) 462 cm2
(ii) 294 cm2
(iii) 588 cm2
(iv) 158 cm2
Answers
Answer:
A. 968m2
B. 29 m
c.44n
d.462cm2
(a) 968m²
(b) 29 m
(c) 44π
(d) 462cm²
Curved surface area:
Diameter = 44 m
Radius = 22 m
Curved surface area of hemispherical dome = 2πr²
= 2πr² = 2π(22)²
= 968m²
Height of the cuboid:
Total height of the monument = 51 m
Radius of hemispherical dome part = height of hemispherical dome = 22m
Height of the cuboidal part = 51 m - 22 m = 29m
Circumference of the base:
Circumference of the base of the dome = 2πr
= 44π
Total surface area of hemispherical dome:
Total surface area of hemispherical dome = 3πr²
= 3 x 22/7 x 7 x 7
= 462cm²