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mschmindy
26.02.2021 •
Mathematics
Shape S below is exactly one quarter of a solid sphere, centre O.
The volume of shape S is 19447 cm
O
Find the surface area of S.
Give your answer correct to 3 significant figures.
You must show your working.
+
Shapes
Volume of sphere =
1 / 놓자
Surface area of sphere = 4ter?
Total marks: 5
Solved
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Ответ:
2,040 cm²
Step-by-step explanation:
Given:
Volume of quarter sphere = 1,944π cm³
Required:
Surface area
Solution:
✔️First, find the radius (r).
Volume of the quarter sphere = ¼(⁴/3πr³)
Thus:
1944π = ¼(⁴/3×π×r³)
1944π = ⅓×π×r³
Multiply both sides by 3
1944π×3 = 1×π×r³
5,832π = πr³
Divide both sides by π
5,832π/π = r³
5,832 = r³
Find the cube root of both sides
r = 18
Radius = 18 cm
✔️Find the surface area of the quarter sphere
Surface area of quarter sphere = ¼ of 4πr² + 2(½ of πr²)
Radius (r) = 18 cm
Plug in the values
Surface area of quarter sphere = ¼×4×π×18² + 2(½×π×18²)
= π×18² + π×18²
= 2,035.75204 ≈ 2,040 cm² (to 3 SF)
Ответ:
The first step in estimating a sum or a difference is to round the numbers, by changing them to the nearest power of ten, hundred, thousand, etc. Round the numbers first, then use mental math to estimate an answer. When rounding, follow these rounding rules: If the number being rounded is less than 5, round down.
Step-by-step explanation: