This document contains solutions to 10 math word problems involving calculations of volumes, areas, ratios of dimensions, etc. for geometric shapes like cylinders, cones, cubes, rectangular prisms. Each problem is solved with the step-by-step working and the final answer is provided as one of the multiple choice options. Common shapes considered include cubes, cylinders, cones, rectangular boxes and prisms. Calculations involve formulas for volumes and surface areas of these standard shapes.

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.