please answer! it's really important
Answers
Solution!!
You need to remember some formulae to solve these kind of questions.
Total surface area (TSA) = 2πrh + 2πr²
Curved surface area (CSA) = 2πrh
The total surface area and the curved surface area of the cylinder are given.
TSA = 462 cm²
CSA = 1/3 of TSA = TSA/3
CSA = 462/3 cm² = 154 cm²
Let's find out the radius first.
TSA = 2πrh + 2πr²
2πrh is the CSA so we can directly put the value of it.
462 cm² = 154 cm² + 2πr²
462 cm² - 154 cm² = 2πr²
308 cm² = 2πr²
308/2 cm² = πr²
154 cm² = (22/7) × r²
154 cm² × (7/22) = r²
7 cm² × 7 = r²
49 cm² = r²
√49 cm² = r
r = 7 cm
Now that we know the radius, we can find out the height by putting the value in the CSA formula.
CSA = 2πrh
154 cm² = 2 × (22/7) × 7 cm × h
154 cm² = 2 × 22 cm × h
154 cm² = 44 cm × h
(154 cm²) ÷ (44 cm) = h
h = 3.5 cm