NCERT Class 10 Chapter 10 Surface Areas and Volumes Official CBSE Board Sample Problems Very Short Answer (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question

A right circular cone of radius 3 cm, has a curved surface area of. Find the volume of the cone, (use )

Solution

Radius of cone (r) = 3 cm

Curved surface area

, , where slant height of cone

We know that,

Volume of cone

Question

In Figure, a decorative block, made up of two solids a cube and a hemisphere. The base of the block is a cube of side 6 cm and the hemisphere fixed on the top has a diameter of 3.5 cm. Find the total surface area of the block. (use )

Solution

Side of the cube = 6 cm

Total surface area of cube

Area covered on the face of cube by circular part of hemisphere

Curved surface area of hemisphere

So, Total surface area of the block Surface area of cube Area of circular face of hemisphere

Curved surface area of hemisphere

Question

1.2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of

The resulting cuboid.

Ans. Abbreviation: CSA = C

Solution

Abbreviation: CSA = Curved Surface Area TSA = Total Surface Area

V = Volume

Volume of cube

According to question, (Side) = 64

= 4

For the resulting cuboid, length , breadth = 4 cm and height = 4 cm

Surface area of resulting cuboid =

Question

If we reduce the height of a cylinder by ′ 4 and double the radius, what will be the impact on the volume?

Solution

Volume of cylinder

Volume of New cylinder

So volume remains same.