Question
A storage container consists of a box of length 90 cm, width 42 cm and height 34 cm, and a lid in the shape of a half-cylinder, as shown in the diagram. The lid fits the top of the box exactly. The
total exterior surface of the storage container is to be painted.
Find the area to be painted. diagram not to scale
Answer/Explanation
\(2\times 90\times\times 34 =6120\) AND \(2\times 42\times 34=2856\)
\(r=21\)
\(21\Pi \times 90 =(1890\Pi , 5937.61..)\rightarrow 20100 cm2 (20079.0…)\)
use of curved surface area formula
\(\Pi \times 21^{2}\rightarrow (441\Pi ,1385.44..)\)
Question
Consider the function f (x) = ax 2 + bx + c . The graph of y = f (x) is shown in the diagram. The vertex of the graph has coordinates (0.5, −12.5) . The graph intersects the x-axis at two points, (−2, 0) and ( p, 0).
a. Find the value of p . [1]
b. Find the value of
(i)a .
(ii)b .
(iii) c . [5]
c. Write down the equation of the axis of symmetry of the graph. [1]
Answer/Explanation
(a) 3
(b) METHOD 1
\(0 = 4a -2b+c\),
\(0 = 9a+ 3b+ c\)
\(- \frac{25}{2}= \frac{1}{4}a + \frac{1}{2}\) b + c\)
on solving we get a , b , c
(i) 2 (ii) – 2(iii) -12
METHOD 2 \(−12.5 = a (0.5+ 2)(0.5- 2)\) (i) \(a=2\)
\(0 = 2x(3)2+ 3b + c \)
\(0 = 2x(-2)2+ (-2b)+c\)
(ii) b = −2(iii) c = −12
(c) x = 0.5