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Surface Area is the area of the outer part of any 3D figure and Volume is the capacity of the figure i.e. the space inside the solid. To find the surface areas and volumes of the combination of solids, we must know the surface area and volume of the solids separately. Some of the formulas of solids are -
√3
l = edge of the cube
l = length
b = breadth
h = height
r = radius
R = outer radius
r = inner radius
l = slant height
If a solid is molded by two or more than two solids then we need to divide it in separate solids to calculate its surface area.
Find the total surface area of the given figure.
This solid is the combination of three solids i.e.cone, cylinder and hemisphere.
Total surface area of the solid = Curved surface area of cone + Curved surface area of cylinder + Curved surface area of hemisphere
Curved surface area of cone
Given, h = 5cm, r = 3cm (half of the diameter of hemisphere)
Curved surface area of cylinder = 2πrh
Given, h = 8cm (Total height – height of cone – height of hemisphere), r = 3cm
Curved surface area of hemisphere = 2πr2
Given, r = 3 cm
Total surface area of the solid
Find the volume of the given solid.
The given solid is made up of two solids i.e. Pyramid and cuboid.
Total volume of the solid = Volume of pyramid + Volume of cuboid
Volume of pyramid = 1/3 Area of base x height
Given, height = 6 in. and length of side = 4 in.
Volume of cuboid = lbh
Given, l = 4 in., b = 4 in, h = 5 in.
Total volume of the solid = 1/3 Area of base x height + lbh
= 1/3 x 4 x 4 x 6 + (4) (4) (5)
= 32 + 80
= 112 in3
When we convert a solid of any shape into another shape by melting or remoulding then the volume of the solid remains the same even after the conversion of shape.
If we transfer the water from a cuboid-shaped container of 20 m x 22 m into a cylindrical container having a diameter of 2 m and height of 3.5 m. then what will be the height of the water level in the cuboid container if the cylindrical tank gets filled after transferring the water.
We know that the volume of the cuboid is equal to the volume of the cylinder.
Volume of cuboid = volume of cylinder
l x b x h = πr2h
20 x 22 x h = 22/7 x 1 x 3.5
440 × h =11
H = 2.5 cm
If we cut the cone with a plane which is parallel to its base and remove the cone then the remaining piece will be the Frustum of a Cone.
Find the lateral surface area of the given frustum of a right circular cone.
Given, r =1.8 in.
R = 4 in.
l = 4.5 in.
The lateral surface area of the frustum of the cone = πl (R + r)
= π x 4.5 (4 +1.8)
=3.14 x 4.5 x 5.8
= 81.95 sq. in.
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