NCERT-CLASSS-10-VOLUME-AND-SURFACE-AREA-1

 SURFACE AREAS AND VOLUMES

 

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                                                    EXERCISE 12.1

Q1: 2 cubes, each of volume 64 cm^3, are joined end to end. Find the surface area of the resulting cuboid.

Solution:

Volume of one cube = X³

Side of one cube = (X³)^1/3

  

If we join two cubes, then it will form a cuboid.

Then the length of the cuboid = 4 cm + 4cm = 8cm.

Height of the cuboid = 4cm

Width = 4cm

Therefore, the total surface area of the cuboid = 2(lb + b*h + h*l)

                                                                                    =2*(8*4 +4*4+4*8)

                                                                                    = 2*(32 + 16 + 32)

                                                                                    = 160 cm²

2. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm, and the total height of the vessel is 13 cm. Find the inner surface area of the vessel.

Solution

Diameter of hemisphere = 2r = 14cm

Radius = 14/2 = 7cm

Total height of the container = 13cm

Height of the cylindrical part = 13-7 cm = 6cm

Inner surface area total = curved surface area of hemisphere curved surface area of cylinder

                                       = 2∏r + 2∏rh = 2∏r(r + h)

                                       = 2*(22/7)*7(7+6)

                                         = 2 * 22 * 13 = 2 * 286

                                         = 572 cm²

 

3. A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of the same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Solution: 

Given radius of the hemisphere = 3.5 cm 

Total height = 15,5 cm 

Heihjt of conical part = 15,5 – 3,5 = 12cm

Slant height of cone = 

Slant height l = 12.5 cm

Total surface area = curved surface area of the hemisphere Curved surface area  of the cone

                             = 2 ∏r²+∏rl = ∏r ( r +l)

                              = 2*(22/7)*3.5 * (3.5 +12.5)

                                = 2*11*16

                                = 356 cm²

4. A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

Solution :

  Greatest diameter = 2r = 7 cm

                               r = 3.5 cm

Total surface area = surface area of five sides of the square + (area of the square - area of the bottom of the hemisphere that covers the top of the cube + curved surface area of the hemisphere

 = 2∏r²+ 6a² - ∏(r)²

^{= 6a + ∏(r)²}

Where ‘a is the side of the cube.

= 6 * 7 * 7 + (22/7)*3.5*3.5

= 294 + 38.5

= 277 cm²

 5. A hemispherical depression is cut out from one face of a cubical wooden block, such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.           

Solution: 

Diameter of the hemisphere = l 

Side of the cubical block = l

Radius of the Hemisphäre = l/2

Total surface area = total surface area of the cube + Total surface area of the hemisphere - base area of the hemisphere

Question 6: A medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see Fig. 12.10). The length of the entire capsule is 14 mm and the diameter of the capsule is 5 mm. Find its surface area.

Question 7:    A tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m, respectively, and the slant height of the top is 2.8 m, find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of 500 per m2. (Note that the base of the tent will not be covered with canvas.)

                              

Solution: 

Question 8: From a solid cylinder, whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest cm².

Solution: 

Question 9: A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 12.11. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the cylinder.