1. A rectangular box has dimensions 1.6 m × 1 m × 0.6 m. How many cubical boxes each of side 20 cm can be fit inside the rectangular box?
A. 220
B. 205
C. 120
D. 165
Answer: Option C
Explanation: a + b = 6
20 cm = 0.2 m
So number of boxes that can fit = 1.6 × 1 × [latex]\frac{0.6 }{0.2}[/latex] × 0.2 × 0.2
2. What is the volume of a cylinder whose curved surface area is 704 c[latex]{m }^{2}[/latex] and height is 14 cm?
A. 2878 c[latex]{m }^{3[/latex]
B. 2914 c[latex]{m }^{3}[/latex]
C. 2396 c[latex]{m }^{3}[/latex]
D. 2816 c[latex]{m }^{3}[/latex]
Answer: Option D
Explanation:
2ᴨrh = 704, h = 14
Solve both, so r = 8
Volume = ᴨ[latex]{r}^{2[/latex]h
3. The total cost of painting the walls of a room is Rs 475. Find the cost of painting the walls of another room whose length, breadth and height each are double than the dimensions of the previous room.
A. Rs 1780
B. Rs 1900
C. Rs 1846
D. Rs 1960
Answer: Option B
Area of first room = 2(l+b)*h
After all dimensions doubled, new area = 2(2l + 2b)*2h = 4[2(l+b)*h ] = 4 times previous area, so cost of painting = 4*475
4. A circular wire of diameter 84 cm is bent into a rectangle with sides ratio 6 : 5. What are the respective sides of the rectangle?
A. 60 cm, 72 cm
B. 78 cm, 65 cm
C. 72 cm, 60 cm
D. 72 cm, 60 cm
Answer: Option C
Explanation:
Length of wire = 2ᴨr = 2([latex]\frac{22}{7}[/latex])*42 = 264 cm
Perimeter of rectangle = 2(6x + 5x) = 264
Solve, x = 12
So dimensions – 12*6, 12*5
5. The ratio of the outer and the inner perimeters of a circular path is 9 : 8. The path is 3 metres wide. What is the diameter of the outer circle?
A. 20 m
B. 27 m
C. 35 m
D. 39 m
Answer: Option B
Explanation:
[latex]\frac{2ᴨr}{2ᴨR }[/latex] = [latex]\frac{9}{8}[/latex]
So [latex]\frac{r}{R}[/latex] = [latex]\frac{9}{8}[/latex], so r = ([latex]\frac{9}{8}[/latex])R
r - R = 3, so ([latex]\frac{9}{8}[/latex])R – R = 3
R = 24, so r = ([latex]\frac{9}{8}[/latex])*24 = 27