A bucket has a diameter of top and bottom of 44cm and 24 cm.find capacity in litres if its 36cm deep
71.03litres
find the average area of the top and bottom
multiply by the height
... this is the volume in cm^3
divide by 1000 to find litres
To find the capacity of a bucket, we need to calculate the volume of the bucket.
Step 1: Calculate the radius of the top and bottom of the bucket.
The radius (r) is equal to half of the diameter (d).
For the top of the bucket: radius (r1) = 44 cm / 2 = 22 cm
For the bottom of the bucket: radius (r2) = 24 cm / 2 = 12 cm
Step 2: Calculate the volume of the bucket using the formula for the volume of a frustum of a cone.
The volume (V) of a frustum of a cone is given by the formula:
V = (h/3) * (A1 + A2 + sqrt(A1 * A2))
where h is the height (depth) and A1 and A2 are the areas of the top and bottom circles, respectively.
Step 3: Calculate the areas of the top and bottom circles.
The area (A) of a circle is given by the formula:
A = π * r^2, where π is approximately 3.14159.
For the top of the bucket: A1 = π * r1^2 = 3.14159 * (22 cm)^2
For the bottom of the bucket: A2 = π * r2^2 = 3.14159 * (12 cm)^2
Step 4: Calculate the volume of the bucket.
V = (h/3) * (A1 + A2 + sqrt(A1 * A2))
V = (36 cm / 3) * (A1 + A2 + sqrt(A1 * A2))
Now, let's calculate the volume (V) in liters.
Step 5: Convert the volume from cubic centimeters to liters.
1 liter (L) is equal to 1000 cubic centimeters (cm^3).
V (in liters) = V (in cubic centimeters) / 1000
Once you input the values and calculate, we can determine the capacity of the bucket in liters.
To find the capacity of the bucket in liters, we need to calculate the volume of the bucket. The volume of a cylinder, which is the shape of the bucket, can be calculated by multiplying the cross-sectional area of the base by the height.
First, let's calculate the cross-sectional area of the base of the bucket. The base of the bucket is circular, so its area can be calculated using the formula for the area of a circle: A = πr^2, where A is the area and r is the radius.
Since the diameter of the top and bottom of the bucket is given, we can find the radius by dividing it by 2. So, the radius of the top is 44/2 = 22 cm, and the radius of the bottom is 24/2 = 12 cm.
Next, let's calculate the area of the top base using its radius:
A_top = πr_top^2 = π(22^2) cm^2
Similarly, let's calculate the area of the bottom base using its radius:
A_bottom = πr_bottom^2 = π(12^2) cm^2
The height of the bucket is given as 36 cm.
Now, we have all the values required to calculate the volume of the bucket:
V = (A_top + A_bottom) * height
V = (π(22^2) + π(12^2)) * 36 cm^3
Calculating this equation will give us the volume in cubic centimeters (cm^3). To convert it to liters, we need to divide the result by 1000 since 1 liter is equal to 1000 cm^3.
V_liters = V_cm^3 / 1000
Therefore, to find the capacity of the bucket in liters, substitute the appropriate values into the equation and calculate the result.