Surface Area And Volumes

3. Solution:
The base of the cylindrical glass has a radius = 3 cm
Area of the base will be πr²= 9π cm²
Volume of the cylindrical glass = πr²h
The height of the cylindrical glass = v/πr² = 108π/9π = 12 cm.
The correct option is (A).

4. (a) 24 cm² (b) 24cm³
(c) 120 cm² (d) 120cm³

5. Solution:
Length of the cuboidal gift box = 6cm
Width of the cuboidal gift box = 4cm
Height of the cuboidal gift box = 5cm
The volume of the gift box = length × width × height
= 6cm*4cm*5cm = 120cm³.
The correct option is (d).

6. (a) 800dm (b) 800dm²
(c) 800dm³ (d) 800m

7. Solution:
Length (l) of the rectangular prism = 10 dm
Width (w) of the rectangular prism = 4 dm
Height (h) of the rectangular prism = 2 m
= 2 × 10 dm [10 dm = 1 m] =20dm
Volume of the prism = l × w × h
10dm*4dm*20dm
= 800dm³.
The correct option is (c).

8. (a) 1:1 (b) 3:1
(c) 4:9 (d) 9:1

9. Solution:
Since the cone and the cylinder have the same base area, their radii are the
same.
Therefore, let radius of cone = radius of cylinder= r
Let h1 and h2 be the height of the cone and the cylinder respectively.
Therefore, volume of the cone= 1/3πr²h1
Volume of the cylinder = πr²h2
It is given that the volumes of the cone and the cylinder are equal
Therefore, 1/3πr²h1= πr²h2
 h1= 3h2 => h1/h2 = 3/1
 Thus, the ratio of the heights of the cone and the cylinder is 3:1.
 The correct option is (b).

10. (a) 150cm² (b) 290cm²
(c) 300cm² (d) 580cm²

11. Solution:
The total area to be painted=the surface area of the rectangular box
= 2(lb + bh + lh).
= 2(10×5 + 5×16 + 10×16).
= 2( 50+ 80+160) = 580cm².
The correct option is (d).

12. (a) 32cm³ (b) 36cm³
(c) 42cm³ (d) 46cm³

13. Solution:
Length of each side of small cube = 1 cm
Volume of each cube = 1 cm3
The given rectangular prism is made up of 36 small equal sized cubes.
Volume of 36 cubes = 36 × 1 = 36 cm3
Volume of the rectangular prism = volume of 36 cubes = 36 cm3.
The correct option is (b).

14. (a) 14cm (b) 12cm
(c) 7cm (d) 6cm

15. Solution:
Let the length of the edge of the cube be ‘a’.
It is known that volume of cube = (edge)³
Therefore, (a)³ = 2744cm³
 a = ³√2744cm
 a = ³√2×2×2×7×7×7cm
 a = 2×7cm = 14cm.
The correct option is (a).

17. This is a simple question so students
should try it self.

18. The volume of the box, so formed is
(a) 50cm³ (b) 60cm³
(c) 70cm³ (d) 80cm³

19. Solution:
Volume of 1 cube = 8 cm3
Number of cubes joined together to form the box = 10
Thus, volume of 10 cubes = 10 × 8 cm3 = 80 cm3
Thus, volume of the box = volume of 10 cubes = 80 cm3
The correct answer is (d).

20. THE END.