SURFACE AREA AND VOLUME OF CUBE WORKSHEET

Problem 1 :

Calculate the volume of the cube if its surface is 150 cm². 

Solution

Problem 2 :

The cube has a surface of 600 cm². What is its volume?

Solution

Problem 3 :

We make a box in the shape of a cube with an edge of 12 cm. how many cm² of sheet metal do we need to create a box if we do not make the lid?

Solution

Problem 4 :

If we reduce the length of the cube edge by 30%, this reduced cube has an area of 1176 cm². Specify the edge length and volume of the original cube.

Solution

Problem 5 :

How can you change the edge length of a cube so that the volume is reduced by 40%?

Problem 6 :

A pyramid with a square base has a volume of 120 cubic meters and a height of 10 meters. Find the side length of the square base.

Solution

Problem 7 :

A pyramid with a square base has a volume of 912 cubic feet and a height of 19 feet. Find the side length of the square base

Solution

Problem 8 :

A cube with a surface area of 96 square centimeters is shown. Eight cubes like the one shown are combined to create a larger cube. What is the volume, in cubic centimeters, of the new cube?

Solution

Problem 9 :

Find the volume of the composite solid below.

Solution

Problem 10 :

Two pyramids with square bases have the same volume. One pyramid has a height of 6 centimeters and the area of the base is 36 square centimeters.

a. What is the volume of the pyramids?

b. The base of the other pyramid has a side length of 3 centimeters. What is the height of this pyramid?

Solution

Problem 1 :

Three cubes are joined end to end forming a cuboid. If side of a cube is 2 cm, find the dimensions of the cuboid thus obtained

Solution

Problem 2 :

Find the lateral surface area of a cube, if its diagonal is √6 cm.

Solution

Problem 3 :

Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down into a single cube whose diagonal is 12√3 cm. find the edges of the three cubes.

Solution

Problem 4 :

Volume of a cube is 5832 m³. Find the cost of painting its total surface area at the rate of $3.50 per m².

Solution

Problem 5 :

The cube has a surface area of 216 dm². Calculate:

a)   The area of one wall,

b)   Edge length,

c)   Cube volume.

Solution

Problem 6 :

Find the side length of the cube whose surface area is 54 m²

Solution

Problem 7 :

A container of length 6 cm width 4 cm and height 9 cm is filled with orange juice. If the same amount of juices is to be stored in to a perfect cube shaped container what will be the size of its each side.

Solution

Problem 8 :

The surface area of a cube is 1734 cm². Work out the volume of the cube.

Solution

Problem 9 :

The volume of a cuboid, whose length and breadth are equal, is 72 m³. If the cuboid’s height is 2 m, find its length and its surface area.

Solution

Problem 10 :

A cube, of side length 10 cm, has the same volume as that of a cuboid of height 10 cm and width 8 cm. Find the length and the surface area of the cuboid.

Solution

Problems on finding length of diagonal

1)  Find the value of x.

 Solution

2)  Find the lateral surface area of a cube, if its diagonal is √6 cm.                     Solution

3)  The side length of a cube is 5 meters. What is the length of its diagonal across one of the faces?

 Solution

4)  Find the length of the face diagonal of a cube when the side measures 9 units. Use the diagonal face formula of a cube.                 Solution

Answer key