solid is in the form of a cone mounted on himispher in such away that the Venter of the base of the cone fast coincide with the center of the base of the hemisphere.the radius of hemisphere and height of cone are r each ,radius of base of cone is 1/2r and slant height of cone is l.find surface area and volume of the solid.
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hemisphere: a = 2πr^2, v = 2/3 πr^3
cone: a = 2πrl, v = 1/3 πr^2h
Now plug in your values as needed. What do you get?
To find the surface area and volume of the solid formed by a cone and a hemisphere, we can break it down into two parts: the surface area and volume of the cone, and the surface area and volume of the hemisphere.
1. Surface Area and Volume of the Cone:
The radius of the base of the cone is 1/2r, and the slant height of the cone is l. To find the surface area of the cone, we can use the formula:
Surface Area of Cone = π * radius * (radius + slant height)
Substituting the values, we get:
Surface Area of Cone = π * (1/2r) * (1/2r + l)
To find the volume of the cone, we use the formula:
Volume of Cone = (1/3) * π * radius^2 * height
Substituting the values, we get:
Volume of Cone = (1/3) * π * (1/2r)^2 * l
2. Surface Area and Volume of the Hemisphere:
The radius of the hemisphere is r. To find the surface area of the hemisphere, we use the formula:
Surface Area of Hemisphere = 2 * π * radius^2
Substituting the value, we get:
Surface Area of Hemisphere = 2 * π * r^2
To find the volume of the hemisphere, we use the formula:
Volume of Hemisphere = (2/3) * π * radius^3
Substituting the value, we get:
Volume of Hemisphere = (2/3) * π * r^3
3. Surface Area and Volume of the Solid:
To find the total surface area of the solid, we add the surface area of the cone and the surface area of the hemisphere:
Total Surface Area = Surface Area of Cone + Surface Area of Hemisphere
To find the total volume of the solid, we add the volume of the cone and the volume of the hemisphere:
Total Volume = Volume of Cone + Volume of Hemisphere
Now, you can substitute the respective formulas and calculate the surface area and volume of the solid using the given values.