Worksheet: Surface Area and Volume of a Right Prism

In this worksheet, we will practice finding surface areas and volumes of right prisms.

Q1:

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

• A 90 cm
• B 45 cm
• C 50 cm
• D 30 cm
• E 60 cm

Q2:

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.

Q3:

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

Q4:

A metal cuboid has dimensions of 9 cm, 12 cm, and 2 cm. If it is melted and converted to a cube, how long will one edge of the cube be?

Q5:

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

Q6:

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

Q7:

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

Q8:

A solid metal cuboid whose dimensions are cm, cm, and cm, was melted and made into small cubes. If the edges of the small cubes are cm, how many can be made from the melted cuboid?

Q9:

Two containers are full of mango juice. The first is a cuboid 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?

Q10:

A company is packaging its products into cubic boxes to be shipped. Each cubic box has a side length of in. These smaller boxes are then packed into larger boxes with dimensions of . 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 and the base of the cone touches each of the edges of the face . Find, in terms of , the ratio between the volume of the cone and the volume of the cube.

• A
• B
• C
• D
• E