the diagram below represents a drinking glass of diameter 10cm. it is partially filled to a height of hcm with apple juice.
(a) using 3.14 give an expression in term of h for the volume of juice.
the actual volume of the juice is 0.471 litres.
(b) calculate the value of h.( 1 litre = 1000 cm3
V = 3.14 * r^2 * h
Radius = 1/2 diameter
471 cm^3 = 3.14 * 5^2 * h
Solve for h.
(a) The expression for the volume of juice can be found by using the formula for the volume of a cylinder, which is given by V = πr^2h, where V is the volume, π is approximately equal to 3.14, r is the radius of the glass (half the diameter), and h is the height of the juice.
In this case, the diameter of the glass is given as 10cm, so the radius (r) would be half of that, which is 5cm.
Now, we can substitute these values into the formula:
V = π(5cm)^2h
Simplifying this expression, we have:
V = 3.14 * 25cm^2 * h
(b) Given that the actual volume of the juice is 0.471 liters, or 471 cm^3 (since 1 liter is equal to 1000 cm^3), we can set up the equation:
471 = 3.14 * 25 * h
To find the value of h, divide both sides of the equation by (3.14 * 25):
471 / (3.14 * 25) = h
Simplifying this expression, we get:
h ≈ 1.5 cm
Therefore, the value of h is approximately 1.5 cm.
To find the expression for the volume of juice in terms of height, we need to know the shape of the glass. Assuming it is a cylinder, the volume of a cylinder is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height.
In this case, the diameter of the glass is 10 cm, so the radius (r) is half of that, which is 5 cm (or 0.05 meters).
(a) Using the formula V = πr²h, we can write the expression for the volume of juice as follows:
V = π(0.05)²h
V = 0.0025πh
We know that the actual volume of the juice is 0.471 liters, but we need to convert it to cubic centimeters (cm³) to match the units used in the equation. Since 1 liter is equal to 1000 cm³, we can do the conversion as follows:
0.471 liters * 1000 cm³/liter = 471 cm³
Now we can equate the expression for the volume of juice to the actual volume:
0.0025πh = 471
(b) To calculate the value of h, we can rearrange the equation and solve for h:
h = 471 / (0.0025π)
h ≈ 471 / 0.00785
h ≈ 599.49 cm (rounded to two decimal places)
Therefore, the value of h is approximately 599.49 cm.