A bucket full of water is in the form of a Frustum of a cone. The bottom and top radii of the Frustum are 18cm and 28cm respectively and the vertical depth is 30cm. Calculate the curved surface area, total surface area and volume of the Frustum
40.3cm
40.3
Please can you solve it in a clearer way
I don't understand how you solved it
To calculate the curved surface area, total surface area, and volume of the frustum, we can use the formulas for these measurements.
1. Curved Surface Area (CSA) of a Frustum of a Cone:
The curved surface area of a frustum of a cone is given by the formula:
CSA = π * (r1 + r2) * l
where r1 and r2 are the radii of the bottom and top bases of the frustum, and l is the slant height of the frustum.
Slant height (l) can be calculated using the formula:
l = √[(h^2) + ((r1 - r2)^2)]
where h is the vertical depth of the frustum.
In this case, r1 = 18 cm, r2 = 28 cm, and h = 30 cm.
Plugging these values into the formulas, we can calculate the curved surface area.
2. Total Surface Area (TSA) of a Frustum of a Cone:
The total surface area of a frustum can be calculated by adding the curved surface area to the sum of the areas of the top and bottom bases of the frustum.
The area of a cone is given by the formula:
Area of a cone = π * r^2
where r is the radius of the base of the cone.
Therefore, the total surface area of the frustum can be calculated by:
TSA = CSA + π(r1^2 + r2^2)
Using the given values of r1 and r2, we can calculate the total surface area.
3. Volume of a Frustum of a Cone:
The volume of a frustum of a cone is given by the formula:
Volume = (1/3) * π * h * (r1^2 + r2^2 + (r1 * r2))
where r1 and r2 are the radii of the bottom and top bases of the frustum, and h is the vertical depth of the frustum.
Plugging in the given values, we can calculate the volume of the frustum.
By performing the necessary calculations using the formulas provided, you can find the curved surface area, total surface area, and volume of the frustum.
well, I suspect the curved surface area is 2 pi * (1/2)(18+28) ,the circumference halfway up, times the slant height.
to find slant height
triangle base = 28 - 18 = 10
height = 30 so hypotenuse = sqrt (100+ 900)= 10 sqrt(10)
so area of curved surface = 46 pi * 10sqrt(10)
to get the total add pi (18^2 + 29^2)
The frustrum is the bottom of a cone of height 84. The missing top has height 54.
v = π/3 (28^2*84 - 18^2*54) = 16120π cm^3