Class 10 Mathematics

# Surface Area Volume

## Exercise 13.1 (NCERT)

^{3} are joined end to end. Find the surface area of the resulting cuboid.

**Solution:** Side of cube

Length of new cuboid = 8 cm, height = 4 cm, width = 4 cm

Surface Area can be calculated as follows:

**Alternate Method:**

Surface area of cube = 6 x side^{2}

When two cubes are joined end to end, then out of 12 surfaces; two surfaces are lost due to joint. Thus, we need to take surface area of 10 surfaces and hence surface area can be given as follows:

= 10 x side ^{2}

= 10 x 4^{2} = 160 cm^{2}

**Solution:** Radius = 7 cm

Height of cylindrical portion = 13 – 7 = 6 cm

Curved surface are of cylindrical portion can be calculated as follows:

Curved surface area of hemispherical portion can be calculated as follows:

Total surface are = 308 + 264 = 572 sq cm

**Solution:** Radius of cone = 3.5 cm, height of cone = 15.5 – 3.5 = 12 cm

Slant height of cone can be calculated as follows:

Curved surface area of cone can be calculated as follows:

Curved surface area of hemispherical portion can be calculated as follows:

Hence, total surface area = 137.5 + 77 = 214.5 sq cm

**Solution:** The greatest diameter = side of the cube = 7 cm

Surface Area of Solid = Surface Area of Cube – Surface Area of Base of Hemisphere + Curved Surface Area of hemisphere

Surface Area of Cube = 6 x Side^{2}

= 6 x 7 x 7 = 294 sq cm

Surface Area of Base of Hemisphere

Curved Surface Area of Hemisphere = 2 x 38.5 = 77 sq cm

Total Surface Area = 294 – 38.5 + 77 = 332.5 sq cm

**Solution:** This question can be solved like previous question. Here the curved surface of the hemisphere is a depression, unlike a projection in the previous question

Total Surface Area

**Solution:** Height of Cylinder = 14 – 5 = 9 cm, radius = 2.5 cm

Curved Surface Area of Cylinder

Curved Surface Area of two Hemispheres

Total Surface Area

^{2}. (Note that the base of the tent will not be covered with canvas.)

**Solution:** Radius of cylinder = 2 m, height = 2.1 m and slant height of conical top = 2.8 m

Curved Surface Area of cylindrical portion

Curved Surface Area of conical portion

Total CSA

Cost of canvas = Rate x Surface Area

= 500 x 44 = Rs. 22000

^{2}.

**Solution:** Radius = 0.7 cm and height = 2.4 cm

Total Surface Area of Structure = Curved Surface Area of Cylinder + Area of top of cylinder + Curved Surface Area of Cone

Curved Surface Area of Cylinder

Area of top

Slant height of cone can be calculated as follows:

Curved Surface Area of Cone

Hence, remaining surface area of structure

**Solution:** Radius = 3.5 cm, height = 10 cm

Total Surface Area of Structure = CSA of Cylinder + CSA of two hemispheres

Curved Surface Area of Cylinder

Surface Area of Sphere

Total Surface Area

Next

Exercise 13.2

Exercise 13.3

Exercise 13.4

Exercise 13.5