Question

Students of class 9th of a school had decided to visit the Gol Gumbaz, Bijapur on an educational tour.

The teacher and the students were interested in history as well. The teacher narrated some facts of Gol

Gumbaz of Bijapur, district of Karnataka to her students. Then the teacher said one can find the

combination of solid figures. There are cubical base and hemispherical dome in space. The Colossal

structure is one of the largest dome ever built in the world.

i) Find the surface area of the cubical portion of the Gumbaz excluding the top and bottom if one side is

about 47 m.

(a) 8836 sq. m. (b) 8866 sq. m. (c) 7866 sq. m. (d) 9688 sq. m. (1m)

ii) What is the volume of the cubical portion of the Gumbaz, taking one side as 47 m?

(a) 604856 cu. m (b) 804823 cu. m (c) 103823 cu. m (d) 106823 cu. m (1m)

iii) What is the longest diagonal of the cubic portion of the Gol Gumbaz taking one side as 47 m?

(a)47√3 m (b) 47√2 m (c) 47√5 m (d) √47 m. (1m)

iv) What is the volume of the hemispherical dome, taking diameter of the dome as 42 m?

(a)19404 cu. m (b) 18404 cu. m (c) 16404 cu. m (d) 20404 cu. m​

Answer 1

Answer:

Given:

A structure of cubical base and hemispherical dome

Step-by-step explanation:

To find:

i) surface area of cubical portion excluding top and bottom

   side=47 m

   SURFACE AREA OF A CUBE=6$a^2$

   now surface area excluding top and bottom faces=4$a^2$=4($47^2$)=8836 sq.m.

   ∴i) Answer     a)8836 sq.m.

ii)Volume of cubical portion=$a^3$=$47^3$=103823 cu.m.

∴ ii) answer      c) 103823 cu.m.

iii)Longest diagonal of a cube=$\sqrt{a^{2}+\sqrt{2a^{2} } ^{2} }$=$\sqrt{47^{2}+\sqrt{2(47^{2}) } ^{2} } ^{2} }$=47$\sqrt{3}$m

  ∴Answer       a) 47$\sqrt{3}$ m

iv)volume of hemispherical dome=$\frac{2}{3}$×$\pi$×$(\frac{d}{2} )^{3}$=19404 cu.m.

   diameter=d=42m

    ∴Answer     a)19404 cu.m.

   

Answer 2

Answer:

Step-by-step explanation: