8TH GRADE MATH WORKSHEET 1 ANSWER

About "8th grade math worksheet 1 answer"  

8th grade math worksheet 1 answer :

Here we are going to see 10 practice questions of mixed topics. We have been preparing this set of questions in order to test how you understood the topics.

Practice questions of mixed topics in 8th grade math

Question 1 :

What is the value of square root of 81? 

(A)  81              (B)  3               (C)  9 

Solution :

 √81  =  √(3 ⋅ 3 ⋅ 3 ⋅ 3)

  =  3 

  =  9

Let us see the solution of next problem on "8th grade math worksheet 1 answer".

Question 2 :

Find the area of a right angled triangle, if the radius of the circumcircle is 5 cm and altitude to the hypotenuse is 4 cm. 

(A)   20 cm2              (B)   10 cm2           (C)   30 cm2

Solution :

Let ABC be the right angled triangle right angled at B. Let O be the center of the circumcircle.

Then, O is the midpoint of the hypotenuse AC.

Hence OA  =  OB  =  OC (radius of circle 5 cm)

Hypotenuse AC  =  Diameter of the circle

  =  2 radius of cicumcircle

  =  2  5  =  10 cm

Let BM be the perpendicular from B on AC.

MB  =  4 cm

Area of right angled triangle ABC 

  =  (1/2)  Base  Height 

  =  (1/2)  10  4

  =  20 cm2

Question 3 :

The volume of cubical box is 46.656 cubic meters. Find the length of the side of the cubical box. 

(A)   3.6 m              (B)   5.2 m           (C)   7.8 m

Solution :

Volume of cubical box  =  46.656 cubic meters

a3  =  46.656 

a  =  3.6

Hence side length of cubical box  =  3.6 meter

Question 4 :

The sum of the digits of a two digit number is 15 and if 9 is added to the number the digits are interchanged. Find the required number. 

(A)  78          (B)   87         (C) 96

Solution :

Let "xy" be the two digit number

Sum of the two digit number  =  15

x + y  =  15  -----(1) 

If 19 is added to the number the digits are interchanged.

xy + 9  =  yx

10x + 1y + 9  =  10y + 1x

10x - x + 1y - 10y  =  -9

9x - 9y  =  -9  -----(2) 

(1)⋅9  ==> 9x+9y  =  135  

              9x-9y  =  -9

           ___________

               18x  =  126

                x  =  7

Applying the value of x in the first equation, we get

7 + y  =  15

Subtract 7 on both sides,

y  =  15 - 7 

 y =  8

Hence the required two digit number is 78.

Question 5 :

In a circle with center O and radius 17 cm, PQ is a chord at a distance of 8 cm from the center. Find the length of the chord. 

(A)  30 cm     (B)  15 cm     (C)  24 cm  

Solution :

In a right triangle OCQ,

OQ2  =  OC2 + CQ2

172  =  82 + CQ2

289 - 64  = CQ2

CQ  =  225  ==>  CQ  =  15

PQ  =  2 CQ

  =  2(15)  =  30 cm

Hence the length of chord is 30 cm. 

Question 6 :

The radius and height of a cylinder are in the ratio 5:7 and its volume is 550 cm³ find its radius.

(A)  5 cm     (B)  6 cm     (C)  7 cm  

Solution :

r : h  =  5 : 7

r/h  =  5/7

r  =  5h/7

Volume of cylinder  =  550 cm³

∏r2 h  =  550

(22/7) ⋅ (5h/7)2 h  =  550

h3  =  550 ⋅ (7/22) (49/25)

h3  =  343

h  =  7

r  =  5

Question 7 :

The mean weight of 4 boys is 56 kg and that of 6 girls in 46 kg. find the combined mean weight of 10 students.

(A)  40 kg     (B)  36 kg     (C)  50 kg  

Solution :

Mean weight of 4 boys  =  56 kg

Weight of 4 boys  =  56 (4)  =  224

Mean weight of 6 girls  =  46 kg

Weight of 6 girls  =  46 (6)  =  276

Total weight  =  224  +  276

  =  500

Average weight  =  500/10  =  50 kg

Question 8 :

The arithmetic mean of 8, 10, x and 12 is 9. Find the value of x. 

(A)  6                (B)   8               (C)   9

Solution :

Arithmetic mean  =  9

(8 + 10 + x + 12)/4  =  9

30 + x  =  9(4)

30 + x  =  36

Subtract 30 on both sides

x  =  36 - 30

 x =  6

Question 9 :

Find the number of sides of regular polygon whose exterior angle measure of 45 degree.

Solution :

Sum of the exterior angles of regular polygon = 360°

But each exterior angle = 45°

number of sides of regular polygon = 360° / 45° = 8.

Question 10 :

Simplify the expressions and evaluate them as directed.

x (x-3) + 2 for x = 1 

Solution :

x (x - 3) + 2

x  =  1

  =  1 ( 1 - 3) + 2

  =  1 (-2) + 2

  =  -2 + 2

  =  0

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