the diameter of a can is 8cm the height is 12cm work out how much water is in the can using method V = PI r2h. use 3 as the vaul
1 answer:
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Answer:
V = 1206.3
Step-by-step explanation:
This shape is made up of a cylinder on the bottom and a cone on the top. We'll find the volumes of these shapes separately and then add them together.
Volume of a cylinder = area (of the base) x height
Substitute in the formula for the area of a circle.
V(cylinder) = x h
Substitute in the values for the radius (8) and height (4)
V(cylinder) = x
x 4
Evaluate using a calculator
V(cylinder) = 804.2477
To the nearest tenth, V(cylinder) = 804.2
Volume of a cone = . This is the area of the circular part of the cone (
), multiplied by the height from the point to the base, all divided by 3.
Substitute in the values for the radius of the circle (8) and the height (6)
V(cone) = (On the top it's
x
x 6)
Evaluate using a calculator
V(cone) = 402.1239
To the nearest tenth, V(cone) = 402.1
Total volume = V(cylinder) + V(cone)
= 804.2 + 402.1
= 1206.3
This is a quadratic equation, i.e. an equation involving a polynomial of degree 2. To solve them, you must rearrange them first, so that all terms are on the same side, so we get
i.e. now we're looking for the roots of the polynomial. To find them, we can use the following formula:
where is a compact way to indicate both solutions
and
, while
are the coefficients of the quadratic equation, i.e. we consider the polynomial
.
So, in your case, we have
Plug those values into the formula to get
So, the two solutions are