# Surface Area and Volume of Combination of Solids

#### Summary

Curved surface area (CSA) is the area of the curved surfaces for the solid. The remaining surfaces of the solid are the flat or the non-curved surfaces.

In a cone, the flat surface is the circular area of the base. In a cylinder, the flat surfaces are the top and bottom circular areas. A sphere has no flat surface, whereas a cuboid and a cube have only flat surfaces.

The flat surface area and the CSA of a solid together add up to the total surface area (TSA) for the solid.

Total Surface Area (TSA) = Curved Surface Area (CSA) + Areas of Flat Surfaces.

Diagonal of a cuboid = $\sqrt{{\text{l}}^{\text{2}}\text{+}{\text{b}}^{\text{2}}\text{+}{\text{h}}^{\text{2}}}$ where l = length, b = breadth, h = height.

Diagonal of a cube = √3×a where a is side of a cube.

Area of a four walls of a room = 2(l + b)h where l = length, b = breadth, h = height.

**Hollow cylinder**

Let R and r be the external an internal radii of a hollow cylinder, and h be the height.

1) Thickness of Cylinder = R - r

2) Area of a cross section = π(R^{2} - r^{2})

3) External curved surface area = 2πRh

4) Internal curved surface area = 2πrh

5) Total surface area of a cylinder (TSA) = External curved surface area + Internal curved surface area + Area of two ends.

= 2πRh + 2πrh + 2π(R^{2} - r^{2}) = 2π( Rh + rh + R^{2} - r^{2 })

6) Volume of the material = πR^{2}h - πr^{2}h = π(R^{2} - r^{2})h.

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#### Questions & Answers*arrow_upward*

### 1 . A rectangular sheet of paper of length 28 cm and breadth 22 cm

Answer.

Given rectangular sheet of paper is rolled along its breadth

length = 28 cm breadth = 22 cm

Hence he

### 2 . Radii of two right circular cylinders are in the ratio of 2:3

Answer.

Ratio of radii =
_{}

Let
_{} and
_{}

Ratio of heights =
_{}...

### 3 . Curved surface area of the circumscribed cylinder

Answer.

Let the radius of the sphere = r

Surface area of the sphere = 4?r
^{2}

Radius of the cylind...

### 4 . Find the volume of the double cone.

Answer.

Given that in a right angled triangle, whose sides are 3 cm and 4 cm(other than hypotenuse).

The dou...

### 5 . what is the volume and surface area formula of frustum

volume = 1/3 ? ( r
_{1}
^{2} + r
_{2}
^{2}+r
_{1}* r
_{2}) h

...