Class 8 Cubes and Cube Root

Transcription

1 ID : in-8-cubes-and-cube-root [1] Class 8 Cubes and Cube Root For more such worksheets visit Answer the questions (1) Find the value of A if (2) If you subtract a number x from 15 times that number, and then take the cube of the difference, what will the result be? (3) If you subtract a number x from 14 times that number, and then take the cube of the difference, what will be the result? (4) Find the value of (5) If the surface areas of two cubes are in the ratio 9:49, and the volume of the first cube is 216 m 3, then what is the volume of the second cube? (6) What is the value of (7) There are two numbers such that sum of the numbers is 27 and their difference is 3. Find the difference of their cubes. (8) Solve the following : (9) Find the cube root of 71 correct to three places of decimal. (10) Take a number x, and multiply it with 7. Take the cube of the resulting number. What is the ratio of this number to the cube of the original number? (11) If a cube has a surface area of 4704 m 2, then what is the volume of the cube? (12) If you add a number x with another number that is 14 times the value of x, and then take the cube of the sum, what will be the result? (13) If one face of a cube has an area of 100 m 2, then what is the volume of the cube? (14) The number of people living in a small town is found to be a perfect cube. We know that the number of men in the town is 15653, and the number of women in the town is By an odd coincidence, we count and find that the number of children in the town is also a perfect cube. If we give you a hint that this number is more than 9260, then what is the smallest possible number of children in the town? (15) What is the value of 2017 Edugain ( All Rights Reserved Many more such worksheets can be generated at

2 Answers ID : in-8-cubes-and-cube-root [2] (1) 2 We have been asked to find the value of A from the following equation, ³ (500A) = 10. ³ (500A) = 10 Taking cube both side, (³ (500A)) 3 = (10) 3 500A = A = A = A = A = 2 Therefore, the value of A is 2. (2) 2744x 3 According to the question, the first number is x and the second number is 15 x. Difference of two the numbers = (15 x - x) Cube of the difference = (15 x - x) 3 = (14 x) 3 = 2744 x 3 Therefore, the result will be 2744x 3.

3 ID : in-8-cubes-and-cube-root [3] (3) 2197x 3 According to the question, the first number is x and the second number is 14 x. Difference of the numbers = (14 x - x) Cube of the difference = (14 x - x) 3 = (13 x) 3 = 2197 x 3 Therefore, the result will be 2197x 3. (4) -9 Let's first find all prime factors of = Now, = -1 3 ( ) = -1 3 ( ) = = -9

4 (5) 2744 m 3 ID : in-8-cubes-and-cube-root [4] Let us assume the side of the first cube is a. Let us assume the side of the second cube is b. Surface area of first cube = 6a 2 Surface area of second cube = 6b 2 Ratio of surface area of two cubes = 9:49 Volume of first cube, a 3 = 216 m 3 a 3 = 6 3 a = 6 Now the ratio of surface area of cubes, 6a 2 9 = 6b = b = 9 b = b = b = b 2 b = 14 Volume of second cube, b 3 = (14) 3 = = 2744 Step 5 Therefore, the volume of the second cube is 2744 m 3.

5 ID : in-8-cubes-and-cube-root [5] (6) 7 17 We have been asked to find the value of. Now, = ( (7 7 7) ( ) ) 1 3 = ( (7)3 ) (17) = (( 7 17 ) 3 ) 1 3 = 7 17 Therefore, the value of is 7 17.

6 (7) 1647 ID : in-8-cubes-and-cube-root [6] Let us assume that x and y are the two numbers. According to the question, the sum of two numbers is 27, that is, x + y = (1) And the difference of two numbers is 3, that is, x - y = 3... (2) On adding equations (1) and (2), x + y + x - y = x = 30 x = 15 Step 5 Now using equation (1), x + y = y = 27 y = = 12 Step 6 Now, difference of their cubes = x 3 - y 3 = (15) 3 - (12) 3 = 1647 Step 7 Therefore, the value of the difference of their cubes is (8) = { ( )} 3 = { (1156)} 3 = { (34 2 )} 3 = (34) 3 = (9) 4.141

7 (10) 343:1 ID : in-8-cubes-and-cube-root [7] If we multiply the number x with 7, the resulting number is: 7x. The cube of the resulting number 7x = (7x) 3 = 343x 3 The original number is x. Cube of the original number = x 3. The ratio of the new number to the original number = New number Original number = 343x3 x 3 = Step 5 Therefore, the ratio of the new number to the cube of the original number is 343:1.

8 (11) m 3 ID : in-8-cubes-and-cube-root [8] We need to find the volume of the cube. The volume of a cube with side a is a 3. This means if we can find the value of a, we can easily find the value of the volume of the cube. Let us find the value of the side a of the cube. We have been told that the surface area of the cube is 4704 m 2. Let us use this fact to write an equation and find the value of a. The surface area of the cube with side a = 6a 2. The given surface area of the cube = 4704 m 2. This means, 4704 = 6a 2 a 2 = a 2 = 784 a = 784 a = 28 Now that we know that the value of the side of the cube is 28, let us find the volume of the cube, which is = a 3 = (28) 3 = m 3 Step 5 Therefore, the volume of the cube is m 3.

9 ID : in-8-cubes-and-cube-root [9] (12) 3375x 3 According to the question, the first number is x and the second number is 14 x. Sum of the two numbers = (x + 14 x) Cube of the sum = (x + 14 x) 3 = (15 x) 3 = 3375 x 3 Therefore, the result will be 3375x 3. (13) 1000 m 3 Let us assume that the length of a side of the cube is a. The area of one face of the cube is 100 m 2. As the face of a cube is a square, its area = a 2, where a is the side of the square(cube). 100 = a = a 2 a = 10 m Volume of the cube (V) = a 3, where a is the side of the cube. Volume of the cube = (10) 3 = = 1000 m 3 Therefore, the volume of the cube is 1000 m 3.

10 (14) 9261 ID : in-8-cubes-and-cube-root [10] Total population of the town is a perfect cube. Number of men in the town = Number of women in the town = It is given that the number of children in the village is also the perfect cube, and is more than Let us first find the values of perfect cubes more than Cube root of 9260 = and the perfect cubes more than 9260 will be the cubes of all integers more than , i.e. 21 3, 22 3, 23 3, etc. The population of children will be the smallest value out of 21 3, 22 3, 23 3, etc, for which the total population of the village is a perfect cube. Step 5 Let us see if the population of the children can be 21 3 (= 9261). In this case, the total population of the village will be = = = Since the cube root of is 37, which is an integer, the total population of the village in this case is indeed a perfect cube. Step 6 Therefore, the smallest possible number of children in the village is 21 3 = 9261.

11 ID : in-8-cubes-and-cube-root [11] (15) -3 7 Let's first find prime factors of 54, 54 = Similarly prime factors of 686, 686 = Now, = = = -3 7