SOLVING SIMPLE CUBIC EQUATIONS WORKSHEET

Solve for x :

Problem 1 :

x³ = 64

Solution

Problem 2 :

x³ - 27 = 0

Solution

Problem 3 :

x³ + 216 = 0

Solution

Problem 4 :

x³ = 0

Solution

Problem 5 :

x³ = -125

Solution

Problem 6 :

x³ + 8 = 0

Solution

Problem 7 :

x³ - 1 = 0

Solution

Problem 8 :

x³ = -1000000

Solution

Problem 9 :

x³ = 512

Solution

Problem 10:

x³ + 1 = 0

Solution

Problem 11 :

Solve 2x³ − 12x² + 18x = 0

Solution

Problem 12 :

Solve 36x³ − x = 0

Solution

Problem 13 :

Solve 20x³ + 80x² = -60x

Solution

Problem 14 :

Solve 3x² = 75x⁴

Solution

Problem 15 :

-13x² + 36 = -x⁴

Solution

Problem 16 :

2x³ - x² - 2x = -1

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

Problem 1 :

Find the value of following cube roots:

x = ∛(27 × 2744)

Solution

Problem 2 :

Evaluate 

Solution

Problem 3 :

Two numbers 4x and 5x are such that sum of their cubes is 189. Find x.

Solution

Problem 4 :

The volume of a cube is 5832 m³, find the length of the side.

Solution

Problem 5 :

Three numbers are in the ratio  3 : 4 : 5. If the sum of their cubes -1728, find the three numbers.

Solution

Problem 6 :

Check whether 648 is a perfect cube or not.

Solution

Problem 7 :

Three numbers are to one another as 2:3:4. The sum of their cubes is 33957. Find the numbers.

Solution

Problem 8 :

Solution

Problem 9 :

If y = 5, then what is the value of 10y√(y³ - y²) ?

Solution

Problem 10 :

Solution

Problem 11 :

Divide the number 26244 by the smallest number so that the quotient is a perfect cube, so he smallest number is :

a) 4     b) 6      c) 36      d) 16

Solution

Problem 12 :

The perfect cube nearest to 2750 is :

a) 2749     b) 2747      c) 2744      d) 2754

Solution

Problem 13 :

Three numbers are in the ratio 1 : 2 : 3. The sum of their cubes is 98784. Find the numbers.

Solution

Problem 14 :

Three numbers are in the ratio 2 : 3 : 4. The sum of their cubes is 33957. Find the numbers.

Solution

Problem 15 :

Find the smallest number to be multiplied with 3600 will make the product perfect cube. Further find the cube root of the product.

Solution