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Science & Math for K6 - K12 Students

Exercises - X,XI &XII
Exercise-X
1. C is a point on such that AC = AD. If the length of CD = 3p + 6 and the length of AD is 60''. What is the value of p?
 Sol: AC = AD AD = 60'' AC = × 60'' = 15'' CD = 60'' – 15'' = 45'' CD = 3p + 6'' = 45'' 3p + 6'' = 45'' 3p = 45 – 6 3p = 39 p = 13''

2. If 5x + 3y = 60 and Then the value of y is
 Sol: 5x + 3y = 60 and

3. If = 4, what is the value of x?
 Sol: = 4 = 4 = 4 x – 6 = 4(x – 2) x – 6 = 4x – 8 4x – x = 8 – 6 3x = 2 x = = 0.6666 x = 0.67

4. 24 steel containers can contain 204 litres of water. What is the volume of water that can be stored in each steel container.
 Sol: Number of steel containers = 24 Total volume of water = 204litres volume of water in each container = = = 8.5 litres

5. f(x) = ax + b. If f(5) = 20, f(3) = 14, what is the volume of ?
 Sol: f(x) = ax + b f(5) = a(5) + b 5a + b = 20 f(3) = a(3) + b 3a + b = 14

6. In v = u + at, if v = 100, u = 64, t = 8 then the value of a is
 Sol: v = u + at 100 = 64 + a(8) 100 – 64 = 8a 8a = 36 a = a = = 4.5

7.
The circumference of each circle is 14π''. What is perimeter of the square?
 Sol: 2πr = 14π r = 7'' side of each square = 2r = 2 × 7 = 14'' perimeter of square = 14'' × 4 = 56''

8.
ABCD is a rectangle 2AB = 4BC = 28''. Find the perimeter of the given figure.
 Sol: 2AB = 28'' AB = 14'' R = 7'' 4BC = 28'' BC = 7'' r = perimeter = πR × 4 + πr × 4 = = 88'' + 44'' = 132''

9.
Circumference of each circle is 88''. What is the altitude of ΔABC?
 Sol: 2πr = 88 r = r = 14'' Side of ΔABC = 14 × 2 = 28'' Height of ΔABC = = √3 × 14 = 1.7 × 14 = 23.8''
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