Question
The diameter of a spherical planet is 6 x 104 km .
(a) Write down the radius of the planet.[1]
The volume of the planet can be expressed in the form π(a × 10k) km3 where 1 ≤ a <10 and k ∈ \(\mathbb{Z}\)
(b) Find the value of a and the value of k . [3]
Answer/Explanation
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Question
estion
Let A(2, -3, 5) and B(-1, 1 , 5). Find
(a) the distance between A and B
(b) the distance between O and B
(c) the coordinates of the midpoint M of the line segment [AB]
(d) the coordinates of point C given that B is the midpoint of [AC].
Answer/Explanation
Ans
(a) \(d_{AB}=\sqrt{3^2+4^2+0^2}=5\)
(b) \(d_{OB}=\sqrt{1^2+1^2+5^2}=\sqrt{27}=3\sqrt{3}\)
(c) M(1/2, -1,5)
(d) C(-4,5,5)
Question
Complete the table
Answer/Explanation
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Question
For a right pyramid of square base of slide 8 and vertical height 3 find
(a) the volume
(b) the surface are
Answer/Explanation
Ans
(a) \(V=\frac{1}{3}8^23=64\)
(b) \(AM^2=4^2+3^2 \Rightarrow AM =5\)
\(S=8^2+4 \times (\frac{1}{2} \times 8 \times 5)=64+80=144\)