Question

formulas of chapter volume and surface area of solids

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Answer 1

CUBOID

• Let length = l, breadth = b and height = h units. Then

• Volume = (l x b x h) cubic units.

• Surface area = 2(lb + bh + lh) sq. units.

• Diagonal = l2 + b2 + h2 units.

CUBE

• Let each edge of a cube be of length a. Then,

• Volume = a3 cubic units.

• Surface area = 6a2 sq. units.

• Diagonal = 3a units.

CYLINDER

• Let radius of base = r and Height (or length) = h. Then,

• Volume = (r2h) cubic units.

• Curved surface area = (2rh) sq. units.

• Total surface area = 2r(h + r) sq. units.

CONE

• Let radius of base = r and Height = h. Then,

• Slant height, l = h2 + r2 units.

• Volume = r2h cubic units.

• Curved surface area = (rl) sq. units.

• Total surface area = (rl + r2) sq. units.

SPHERE

• Let the radius of the sphere be r. Then,

• Volume = r3 cubic units.

• Surface area = (4r2) sq. units.

HEMISPHERE

• Let the radius of a hemisphere be r. Then,

• Volume = r3 cubic units.

• Curved surface area = (2r2) sq. units.

• Total surface area = (3r2) sq. units.

Note: 1 litre = 1000 cm3.

Answer 2

Answer:

Surface area and volume are calculated for any three-dimensional geometrical shape. The surface area of any given object is the area or region occupied by the surface of the object. Whereas volume is the amount of space available in an object.

In geometry, there are different shapes and sizes such as sphere, cube, cuboid, cone, cylinder, etc. Each shape has its surface area as well as volume. But in the case of two-dimensional figures like square, circle, rectangle, triangle, etc., we can measure only the area covered by these figures and there is no volume available. Now, let us see the formulas of surface areas and volumes for different 3d-shapes.

Learn more: Mathematics Grade 10

Surface Area

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called surface area. It is also measured in square units.

Generally, Area can be of two types:

(i) Total Surface Area

(ii) Curved Surface Area/Lateral Surface Area

Total surface area

Total surface area refers to the area including the base(s) and the curved part. It is total of the area covered by the surface of the object. If the shape has curved surface and base, then total area will be the sum of the two areas.

Curved surface area/Lateral surface area

Curved surface area refers to the area of only the curved part of the shape excluding its base(s). It is also referred to as lateral surface area for shapes such as a cylinder.

Volume

The amount of space, measured in cubic units, that an object or substance occupies is called volume. Two-dimensional doesn’t have volume but has area only. Example, Volume of Circle cannot be found, though Volume of the sphere can be. It is so because a sphere is a three-dimensional shape.

Explanation:

What are the formulas for surface area and volume of cuboid?

Surface area of cuboid = 2(b+bh+hl)

Volume = l × b × h

where l = length, b=breadth and h = height.

What is the total surface area of cylinder?

Total surface area of cylinder = 2 π r(r+h), where r is the radius of the circular base and h is the height of the cylinder.

How to calculate the volume of a cone-shaped object?

If r is the radius of circular base of the cone-shaped object and h is the height, then the formula to find the volume of the cone is given by: V = 1/3π r2 h

What is the total surface area of hemisphere?

The total surface area of hemisphere is equal to sum of half of surface area of sphere and area of its circular base.

Total surface area of hemisphere = 2 π r2+ π r2 = 3 π r2