Answer:
(i) The volume of each hemispherical bowl can be calculated as follows:
Volume of a hemispherical bowl = (2/3) x pi x (d/2)^3, where d is the internal diameter of the bowl.
Substituting d = 21 cm, we get:
Volume of a hemispherical bowl = (2/3) x pi x (21/2)^3 = 4851.97 cubic centimeters
The total volume of compost required to fill all 16 bowls is therefore:
Total volume of compost = 16 x 4851.97 = 77631.52 cubic centimeters
If 1 cm³ of compost weighs 2.31 gm, then the total weight of required compost is:
Total weight of compost = 77631.52 x 2.31 = 179231.83 grams or 179.23 kilograms
Therefore, Mrs. Thapa would need 179.23 kilograms of compost to fill all 16 hemispherical bowls.
(ii) The outer curved surface area of each hemispherical bowl can be calculated as follows:
Outer curved surface area of a hemispherical bowl = 2 x pi x (d/2)^2, where d is the internal diameter of the bowl.
Substituting d = 21 cm, we get:
Outer curved surface area of a hemispherical bowl = 2 x pi x (21/2)^2 = 693.84 square centimeters
The total outer curved surface area of all 16 bowls is therefore:
Total outer curved surface area = 16 x 693.84 = 11101.44 square centimeters
If Mrs. Thapa covers the outer curved surface of each bowl with polythene sheet, then the total amount of polythene required would be equal to the total outer curved surface area of all 16 bowls.
Therefore, the total amount of polythene required would be 11101.44 square centimeters.
Explanation: