class lX Surface Area and Volume(Part -1)

 

SURFACE AREAS AND VOLUMES

(part 1)

Surface Area of a Cuboid = 2(lb + bh + hl)

Surface Area of a Cube = 6a ²

Lateral surface area of the cuboid=2(l + b) h

Lateral surface area of a cube = 4a²

Curved Surface Area of a Cylinder = 2πrh

Total Surface Area of a Cylinder = 2πr(r + h)

Curved Surface Area of a Cone = πrl

Total Surface Area of a Cone = πr(l + r)

Surface Area of a Sphere = 4 π r ²

Curved Surface Area of a Hemisphere = 2πr ²

Total Surface Area of a Hemisphere = 3πr ²

 

^{Important questions}

1. The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ` 10 per m² is Rs 15000, find the height of the hall.

2. A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape. It is 30 cm long, 25 cm wide and 25 cm high.

(i)What is the area of the glass?

(ii) How much of tape is needed for all the 12 edges?

3. Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5 m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm (see Fig.). Find how much he would spend for the tiles, if the cost of the tiles is ` 360 per dozen.

4.The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m² .

 

5. Find

(i) The lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high.

(ii)   How much steel was actually used, if 1/ 12 of the steel actually used was wasted in making the tank?

 

6. What length of tarpaulin 3 m wide will be required to make conical tent of height 8 m and base radius 6 m? Assume that the extra length of material that will be required for stitching margins and wastage in cutting is approximately 20 cm (Use π = 3.14).

 

7. A conical tent is 10 m high and the radius of its base is 24 m. Find

 (i) Slant height of the tent.

(ii) Cost of the canvas required to make the tent, if the cost of 1 m² canvas is Rs 70.

8. The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas?

 

9. The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

10. A right circular cylinder just encloses a sphere of radius r (see Fig.).

Find

 (i) surface area of the sphere,                                                            

 (ii) curved surface area of the cylinder,

 (iii) Ratio of the areas obtained in (i) and (ii)

Credit : ncert.nic.in