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Browse complete papersA cone is melted and recast into smaller cones with \(\frac{1}{3}\) the radius and \(\frac{1}{3}\) the height. How many cones are formed?
27
30
32
25
Correct answer
27
A cone is cut by a plane that runs parallel to its base, creating a smaller cone that is similar to the original cone. If the height of this smaller cone is one-third that of the original cone, what is the ratio of their volumes?
1 : 3
1 : 9
1 : 27
1 : 6
Correct answer
1 : 3
Expand : (2x - 3)2
4x2 + 12x + 9
4x2 - 12x + 9
4x2 - 14x + 10
4x2 + 10x + 9
Correct answer
4x2 + 12x + 9
A machine processes 2.4 items per second. How many items does it process in 2\(\frac{1}{2}\) minutes?
360
380
300
420
Correct answer
360
The base of a regular right pyramid is a square with the side length of 6 cm. If its volume is 144 cm3, what is its height?
8 cm
10 cm
12 cm
15 cm
Correct answer
8 cm
What is the sum of the exterior angles of a polygon with n sides?
4π
5π
2π
3π
Correct answer
4π
Simplify:
\(\rm (0.625\div 2.5)\left(\frac{5}{8}\times 2\right)=?\)
2.5
2
0.3125
3
Correct answer
2.5
A regular right pyramid has a square base. Its base area is 100 cm2 and its lateral surface area is 260 cm2. What is the height of the pyramid?
10 cm
12 cm
13 cm
15 cm
Correct answer
10 cm
A water pipe supplies water at a constant rate. In 4.5 minutes, it fills \(2\frac{1}{4}\) liters. At this rate, how much time will it take to fill 5.625 liters?
10 minutes
11.25 minutes
12 minutes
12.5 minutes
Correct answer
10 minutes
A farmer uses \(\frac{2}{3}\) of his land for wheat and 0.125 for rice. What fraction remains unused?
\(\frac{1}{6}\)
\(\frac{1}{8}\)
\(\frac{3}{16}\)
\(\frac{5}{24}\)
Correct answer
\(\frac{1}{6}\)