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Worksheet: Surface Area and Volume of a Right Prism

Q1:

Find, to the nearest tenth, the surface area of a right hexagonal prism if its height is 14 centimeters and each of its base edges is 9 centimeters.

Q2:

A metal rectangular prism has dimensions of 9 cm, 12 cm, and 2 cm. If it is melted and converted to a cube, what will the length of the cube be?

  • A 12 cm
  • B 9 cm
  • C 72 cm
  • D 6 cm

Q3:

A silver cube has length 18 cm. It is going to be melted and converted into rectangular prisms with dimensions 3 cm, 2 cm, and 12 cm. How many rectangular prisms will this make?

  • A4
  • B
    5 760
  • C54
  • D81

Q4:

A silver cube with length 36 cm is melted and poured into a rectangular prism-shaped mold whose base measures 36 cm by 18 cm. What is the height of the new silver rectangular prism?

  • A 2 cm
  • B 18 cm
  • C 648 cm
  • D 72 cm

Q5:

A rectangular tank is 90 cm wide and 100 cm long. It can hold up to 810 liters of water when full. If it is filled to one-third of its height, determine the height of the water in centimeters.

Q6:

Given that each unit cube has a side length of 1, find the volume of the given prism.

Q7:

A rectangular prism has a surface area of 382 square inches, a height of 7 inches, and a width of 5 inches. Determine its volume.

Q8:

A solid metal cuboid whose dimensions are 2 π‘₯ cm, 6 π‘₯ cm, and 1 0 π‘₯ cm, was melted and made into small cubes. If the edges of the small cubes are 2 π‘₯ cm, how many can be made from the melted cuboid?

Q9:

Two containers are full of mango juice. The first is a rectangular prism with inner dimensions of 35 cm, 33 cm and 35 cm. The second is a cube with an internal edge length of 30 cm. All of the juice needs to be poured into bottles which have a volume of 775 cm3. How many bottles are required?

  • A53 bottles
  • B35 bottles
  • C18 bottles
  • D87 bottles

Q10:

A company is packaging its products into cubic boxes to be shipped. Each cubic box has a side length of 5 1 4 in. These smaller boxes are then packed into larger boxes with dimensions of 2 1 Γ— 1 0 . 5 Γ— 5 1 4 i n i n i n . How many cubic boxes can be packed into a larger box for shipping?

Q11:

A cubic container with an edge length of 24 cm was full of water which was then poured into a second container. If the new container is a cuboid with base dimensions of 24 cm and 16 cm, what is the height of the water in it?

Q12:

A cube has an edge length of 29 cm, and a cuboid has dimensions 45 cm, 26 cm, and 32 cm. Which has the larger volume?

  • Athe cuboid
  • Bthe cube

Q13:

A cube has an edge length of 15 cm, and a cuboid has dimensions of 19 cm, 15 cm, and 21 cm. What is the difference between their volumes?

Q14:

A right circular cone is placed inside this cube such that the vertex of the cone is at the center of the base 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€² and the base of the cone touches each of the edges of the face 𝐴 𝐡 𝐢 𝐷 . Find, in terms of πœ‹ , the ratio between the volume of the cone and the volume of the cube.

  • A πœ‹ ∢ 4
  • B πœ‹ ∢ 6
  • C πœ‹ ∢ 3
  • D πœ‹ ∢ 1 2
  • E πœ‹ ∢ 2