Ashish is a Class IX student. His class teacher Mrs Verma arranged a historical trip to great Stupa of Sanchi. She explained that Stupa of Sanchi is great example of architecture in India. Its base part is cylindrical in shape. The dome of this stupa is hemispherical in shape, known as Anda. It also contains a cubical shape part called Hermika at the top, Path around Anda is known as Pradakshina Pach (0) (0)
Find the volume of the Hermika, if the side of cubical part is 10 m.
Find the volume of cylindrical base part whose diameter and height 48 m and 14 m.
OR If the diameter of the Anda is 42 m, then find the volume of the Anda.
(5) If the volume of each brick used is 0.01 m², then find the number of bricks used to make th base.
Find the volume of the Hermika, if the side of cubical part is 10 m.
Find the volume of cylindrical base part whose diameter and height 48 m and 14 m.
OR If the diameter of the Anda is 42 m, then find the volume of the Anda.
(5) If the volume of each brick used is 0.01 m², then find the number of bricks used to make th base.
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Answer:
To find the volume of the Hermika (the cubical part at the top of the Stupa), we can use the formula for the volume of a cube:
Volume = side^3
Volume = 10^3 = 1000 m^3
To find the volume of the cylindrical base part, we can use the formula for the volume of a cylinder:
Volume = πr^2h
where r is the radius and h is the height. Given that the diameter of the base is 48m and the height is 14m.
r=48/2 =24m
so the Volume = π24^214 = 25,472 m^3
To find the volume of the Anda (hemispherical part of the dome), we can use the formula for the volume of a hemisphere:
Volume = 2/3πr^3
where r is the radius. Given that the diameter of the Anda is 42m.
r=42/2 =21m
so the Volume = 2/3π21^3 = 22,958.667 m^3
To find the number of bricks used to make the base, we need to know the area of the base. If we assume that the base is circular, and the diameter is 48m, we can use the formula for the area of a circle to find the area of the base:
Area = πr^2
where r is the radius.
r = 48/2 = 24m
so the area = π*24^2 = 1,766.667 m^2
If we assume that each brick has a volume of 0.01 m^2, we can find the number of bricks used by dividing the area of the base by the volume of each brick:
Number of bricks = 1,766.667 m^2 / 0.01 m^2 = 176,666.7
Note that these calculations are based on the assumption that the base of the stupa is circular and the dimensions are given. The actual dimensions and shapes of the stupa may vary, so please verify with your teacher or any other reliable source for more accurate information.
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Step-by-step explanation:
1. To find the volume of the Hermika, we can use the formula for the volume of a cube:
2. To find the volume of the cylindrical base part of the stupa, we can use the formula for the volume of a cylinder:
V = πr^2h
where V is the volume, r is the radius of the cylinder, and h is the height.
Given that the diameter of the cylindrical base is 48 m, so the radius of the cylinder is 48/2 = 24 m
and height of the cylinder is 14 m.
V = π * (24^2) * 14 = (242414*π) = 17616 * π m³
3. To find the volume of the Anda (dome) we can use the formula for the volume of a hemisphere:
V = 2/3 * π * r^3
Given that the diameter of the Anda is 42 m, so the radius of the Anda is 42/2 = 21 m
V = 2/3 * π * (21^3) = 2/3 * π * 9261 = 18485.4 * π m³
4. To find the number of bricks used to make the base, we can use the volume of the cylindrical base part and the volume of each brick:
Number of bricks = V / volume of each brick
Given that the volume of each brick is 0.01 m² and the volume of the cylindrical base is (17616 * π) m³, so
Number of bricks = (17616 * π) / 0.01 = 1.7616 * 10^7
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