Answer: (i) To find the total weight of compost required:
First, find the volume of one bowl: We can use the formula for the volume of a sphere to find the volume of one hemispherical bowl. The radius of the sphere is equal to half the diameter of the bowl, which is 21 cm / 2 = 10.5 cm. The volume of one hemispherical bowl is given by the formula (4/3)πr^3/2, where r is the radius. Plugging in the values, we get:
(4/3)π(10.5)^3/2 = (4/3) * (22/7) * (10.5)^3/2 = 532.8 cm³
Multiply by the number of bowls: To find the total volume of compost required, multiply the volume of one bowl by the number of bowls: 532.8 cm³ * 16 bowls = 8544.8 cm³
Multiply by the weight of compost per cm³: To find the total weight of compost, multiply the total volume by the weight of compost per cm³: 8544.8 cm³ * 2.31 gm/cm³ = 19824.9 gm = 19.82 kg
So, the total weight of compost required is 19.82 kg.
(ii) To find the amount of polythene required:
First, find the circumference of one bowl: The circumference of the circle is equal to 2π times the radius. So, the circumference of one bowl is 2π * 10.5 cm = 21π cm.
Find the length of the polythene: To find the length of the polythene, we need to find the length of the curved surface of the bowl. We can use the formula for the circumference of a circle, which is 2πr, where r is the radius. The curved surface of the bowl is half the circumference of the circle, so the length of the polythene is 21π cm / 2 = 10.5π cm.
Multiply by the number of bowls: To find the total length of the polythene, multiply the length of one bowl by the number of bowls: 10.5π cm * 16 bowls = 168π cm = 528 cm (rounded to the nearest cm)
So, the total amount of polythene required is 528 cm.
Explanation: