### Problem: The three sides (length, width, height) of a Rectangular Prism (i.e. a cuboid) are 38, 36 and 35. What is the (a)Total Surface Area (b)Volume (c)Length of the diagonal?

Solution:

Total Surface Area of the Cuboid (or Rectangular Prism) = 2 x (lw + wh + hl) = 2 x (38 x 36 + 36 x 35 + 35 x 38) = 7916 square inches

Volume of the Cuboid (or Rectangular Prism) = lwh = (38 x 36 x 35 = 47880 cubic inches

Length of the diagonal = (length

^{2} + width

^{2} + height

^{2})

^{0.5} = 3965**0.5 inches

### Problem: The three sides (length, width, height) of a Rectangular Prism (i.e. a cuboid) are 18, 15 and 13. What is the (a)Total Surface Area (b)Volume (c)Length of the diagonal?

Solution:

Total Surface Area of the Cuboid (or Rectangular Prism) = 2 x (lw + wh + hl) = 2 x (18 x 15 + 15 x 13 + 13 x 18) = 1398 square cm

Volume of the Cuboid (or Rectangular Prism) = lwh = (18 x 15 x 13 = 3510 cubic cm

Length of the diagonal = (length

^{2} + width

^{2} + height

^{2})

^{0.5} = 718**0.5 cm

### Problem: The three sides (length, width, height) of a Rectangular Prism (i.e. a cuboid) are 20, 19 and 18. What is the (a)Total Surface Area (b)Volume (c)Length of the diagonal?

Solution:

Total Surface Area of the Cuboid (or Rectangular Prism) = 2 x (lw + wh + hl) = 2 x (20 x 19 + 19 x 18 + 18 x 20) = 2164 square m

Volume of the Cuboid (or Rectangular Prism) = lwh = (20 x 19 x 18 = 6840 cubic m

Length of the diagonal = (length

^{2} + width

^{2} + height

^{2})

^{0.5} = 1085**0.5 m

### Problem: The three sides (length, width, height) of a Rectangular Prism (i.e. a cuboid) are 39, 36 and 35. What is the (a)Total Surface Area (b)Volume (c)Length of the diagonal?

Solution:

Total Surface Area of the Cuboid (or Rectangular Prism) = 2 x (lw + wh + hl) = 2 x (39 x 36 + 36 x 35 + 35 x 39) = 8058 square units

Volume of the Cuboid (or Rectangular Prism) = lwh = (39 x 36 x 35 = 49140 cubic units

Length of the diagonal = (length

^{2} + width

^{2} + height

^{2})

^{0.5} = 4042**0.5 units

### Problem: The three sides (length, width, height) of a Rectangular Prism (i.e. a cuboid) are 15, 14 and 11. What is the (a)Total Surface Area (b)Volume (c)Length of the diagonal?

Solution:

Total Surface Area of the Cuboid (or Rectangular Prism) = 2 x (lw + wh + hl) = 2 x (15 x 14 + 14 x 11 + 11 x 15) = 1058 square inches

Volume of the Cuboid (or Rectangular Prism) = lwh = (15 x 14 x 11 = 2310 cubic inches

Length of the diagonal = (length

^{2} + width

^{2} + height

^{2})

^{0.5} = 542**0.5 inches

### Problem: The length and width (breadth) of a Rectangular Prism (i.e. a cuboid) are 10, 8. The volume is 400 cubic inches. What is the (a)Total Surface Area (b)Length of the diagonal?

Solution:

Volume of the Cuboid (or Rectangular Prism) = lwh => h = Volume/(length x width)= 400 / (10 x 8) = 5 inches

Total Surface Area of the Cuboid (or Rectangular Prism) = 2 x (lw + wh + hl) = 2 x (10 x 8 + 8 x 5 + 5 x 10) = 340 square inches

Length of the diagonal = (length

^{2} + width

^{2} + height

^{2})

^{0.5} = 189**0.5 inches

### Problem: The length and width (breadth) of a Rectangular Prism (i.e. a cuboid) are 20, 19. The volume is 6840 cubic cm. What is the (a)Total Surface Area (b)Length of the diagonal?

Solution:

Volume of the Cuboid (or Rectangular Prism) = lwh => h = Volume/(length x width)= 6840 / (20 x 19) = 18 cm

Total Surface Area of the Cuboid (or Rectangular Prism) = 2 x (lw + wh + hl) = 2 x (20 x 19 + 19 x 18 + 18 x 20) = 2164 square cm

Length of the diagonal = (length

^{2} + width

^{2} + height

^{2})

^{0.5} = 1085**0.5 cm

### Problem: The length and width (breadth) of a Rectangular Prism (i.e. a cuboid) are 33, 32. The volume is 32736 cubic m. What is the (a)Total Surface Area (b)Length of the diagonal?

Solution:

Volume of the Cuboid (or Rectangular Prism) = lwh => h = Volume/(length x width)= 32736 / (33 x 32) = 31 m

Total Surface Area of the Cuboid (or Rectangular Prism) = 2 x (lw + wh + hl) = 2 x (33 x 32 + 32 x 31 + 31 x 33) = 6142 square m

Length of the diagonal = (length

^{2} + width

^{2} + height

^{2})

^{0.5} = 3074**0.5 m

### Problem: The length and width (breadth) of a Rectangular Prism (i.e. a cuboid) are 39, 36. The volume is 46332 cubic units. What is the (a)Total Surface Area (b)Length of the diagonal?

Solution:

Volume of the Cuboid (or Rectangular Prism) = lwh => h = Volume/(length x width)= 46332 / (39 x 36) = 33 units

Total Surface Area of the Cuboid (or Rectangular Prism) = 2 x (lw + wh + hl) = 2 x (39 x 36 + 36 x 33 + 33 x 39) = 7758 square units

Length of the diagonal = (length

^{2} + width

^{2} + height

^{2})

^{0.5} = 3906**0.5 units

### Problem: The length and width (breadth) of a Rectangular Prism (i.e. a cuboid) are 12, 9. The volume is 756 cubic inches. What is the (a)Total Surface Area (b)Length of the diagonal?

Solution:

Volume of the Cuboid (or Rectangular Prism) = lwh => h = Volume/(length x width)= 756 / (12 x 9) = 7 inches

Total Surface Area of the Cuboid (or Rectangular Prism) = 2 x (lw + wh + hl) = 2 x (12 x 9 + 9 x 7 + 7 x 12) = 510 square inches

Length of the diagonal = (length

^{2} + width

^{2} + height

^{2})

^{0.5} = 274**0.5 inches

### Problem: The three sides (length, width, height) of a Hollow Rectangular Prism (i.e. a hollow cuboid) are l = 24, w = 22 and h = 21. If the thickness is t = 2 inches what is the volume of the material used?

Solution:

Volume of the material used in the Cuboid (or Rectangular Prism) = Volume of Outer cuboid - Volumer of inner hollow cuboid

= lwh - (l-2t)(w-2t)(h-2t) = (24 x 22 x 21) - ((24-4) x (22-4) x (21-4)) = 11088 = 4968 cubic inches

### Problem: The three sides (length, width, height) of a Hollow Rectangular Prism (i.e. a hollow cuboid) are l = 22, w = 19 and h = 17. If the thickness is t = 2 cm what is the volume of the material used?

Solution:

Volume of the material used in the Cuboid (or Rectangular Prism) = Volume of Outer cuboid - Volumer of inner hollow cuboid

= lwh - (l-2t)(w-2t)(h-2t) = (22 x 19 x 17) - ((22-4) x (19-4) x (17-4)) = 7106 = 3596 cubic cm

### Problem: The three sides (length, width, height) of a Hollow Rectangular Prism (i.e. a hollow cuboid) are l = 33, w = 30 and h = 28. If the thickness is t = 2 m what is the volume of the material used?

Solution:

Volume of the material used in the Cuboid (or Rectangular Prism) = Volume of Outer cuboid - Volumer of inner hollow cuboid

= lwh - (l-2t)(w-2t)(h-2t) = (33 x 30 x 28) - ((33-4) x (30-4) x (28-4)) = 27720 = 9624 cubic m

### Problem: The three sides (length, width, height) of a Hollow Rectangular Prism (i.e. a hollow cuboid) are l = 27, w = 25 and h = 23. If the thickness is t = 2 units what is the volume of the material used?

Solution:

Volume of the material used in the Cuboid (or Rectangular Prism) = Volume of Outer cuboid - Volumer of inner hollow cuboid

= lwh - (l-2t)(w-2t)(h-2t) = (27 x 25 x 23) - ((27-4) x (25-4) x (23-4)) = 15525 = 6348 cubic units

### Problem: The three sides (length, width, height) of a Hollow Rectangular Prism (i.e. a hollow cuboid) are l = 30, w = 29 and h = 28. If the thickness is t = 2 inches what is the volume of the material used?

Solution:

Volume of the material used in the Cuboid (or Rectangular Prism) = Volume of Outer cuboid - Volumer of inner hollow cuboid

= lwh - (l-2t)(w-2t)(h-2t) = (30 x 29 x 28) - ((30-4) x (29-4) x (28-4)) = 24360 = 8760 cubic inches