1.
What happens to the volume of a cone if its radius is reduced by half and its height is quadrupled?
Correct Answer
D. The volume remains constant
Explanation
When the radius of a cone is reduced by half and its height is quadrupled, the volume of the cone remains constant. This is because the formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height. When the radius is reduced by half, the term (1/3)πr^2 becomes (1/3)π(1/2r)^2 = (1/3)π(1/4)r^2 = (1/12)πr^2. At the same time, when the height is quadrupled, the term h becomes 4h. Therefore, the new volume is (1/12)πr^2 * 4h = (1/3)πr^2h, which is equal to the original volume.
2.
Which is the most accurate instrument of measuring length
Correct Answer
C. Micrometer caliper
Explanation
A micrometer caliper is the most accurate instrument for measuring length because it has a higher precision and can measure to a smaller degree of accuracy compared to other instruments such as a ruler or meterstick. The micrometer caliper has a smaller scale and can measure down to the micrometer level, making it suitable for precise measurements in various fields such as engineering, manufacturing, and scientific research.
3.
A box is 30 cm long, 5 cm wide, and 10 cm high. If it has a mass of 30 g, what is its density?
Correct Answer
D. 20 kg/m3
Explanation
The density of an object is calculated by dividing its mass by its volume. In this case, the mass of the box is given as 30 g. To find the volume, we multiply the length, width, and height of the box, which gives us 30 cm x 5 cm x 10 cm = 1500 cm3. Dividing the mass of 30 g by the volume of 1500 cm3, we get a density of 0.02 g/cm3. However, the answer is given in kg/m3, so we need to convert the units. Since 1 kg = 1000 g and 1 m3 = 1,000,000 cm3, we can convert the density to 0.02 g/cm3 x (1 kg/1000 g) x (1,000,000 cm3/1 m3) = 20 kg/m3.
4.
How many kilograms are there in 73 milligrams
Correct Answer
D. 0.000073 kg
Explanation
There are 1000 milligrams in 1 gram, and 1000 grams in 1 kilogram. Therefore, to convert milligrams to kilograms, we divide by 1,000,000 (1000 x 1000). In this case, 73 milligrams divided by 1,000,000 equals 0.000073 kilograms.
5.
How many grams are there in 5,000 mg
Correct Answer
C. 5
Explanation
There are 1000 milligrams (mg) in one gram. Therefore, to convert mg to grams, we divide the number of mg by 1000. In this case, we have 5,000 mg, so we divide 5,000 by 1000 to get 5 grams.
6.
What is the area of a cube if the sides of the cube is 4
Correct Answer
C. 64
Explanation
The area of a cube is found by multiplying the length of one side by itself. In this case, the length of one side is given as 4. So, the area of the cube would be 4 * 4 = 16.
7.
Which of the following is a scalar
Correct Answer
A. Temperature
Explanation
Temperature is a scalar quantity because it only has magnitude and no direction. Scalar quantities are those that can be fully described by their magnitude alone, such as temperature, mass, and time. On the other hand, force, acceleration, and velocity are vector quantities because they have both magnitude and direction.
8.
A quantity completely specified by means of magnitude and direction
Correct Answer
B. Vector
Explanation
A vector is a quantity that is completely specified by its magnitude (or size) and its direction. This means that in order to fully describe a vector, you need to know both how big it is and in which direction it is pointing. In contrast, other options like graph, speed, and distance do not have a direction associated with them and therefore do not fit the definition of a vector.
9.
The property of a body that causes it to have weight in a gravitational field
Correct Answer
A. Mass
mass
Explanation
Mass is the property of a body that causes it to have weight in a gravitational field. Weight is the force exerted on an object due to gravity, and it is directly proportional to the mass of the object. Therefore, the correct answer is mass.
10.
It is possible to get the volume of an 8.5 x 11 cm bond paper with a micrometer caliper
Correct Answer
B. False
11.
What is the volume of a cylinder that has a diameter of 6 cm and a height of 3 in cubic centimeters?
Correct Answer
B. 84.8
Explanation
The volume of a cylinder is calculated using the formula V = πr^2h, where r is the radius of the base and h is the height. In this case, the diameter is given as 6 cm, so the radius would be half of that, which is 3 cm. The height is given as 3 cm. Plugging these values into the formula, we get V = π(3^2)(3) = 27π ≈ 84.8 cubic centimeters.
12.
What is the volume of a rectangular solid that has a length of 500 cm, width of 0.001 km and a height of 2 meters
Correct Answer
D. 10
Explanation
The volume of a rectangular solid is calculated by multiplying its length, width, and height. In this case, the length is given as 500 cm, the width is given as 0.001 km (which is equal to 100 cm), and the height is given as 2 meters (which is equal to 200 cm). Multiplying these values together, we get 500 cm * 100 cm * 200 cm = 10,000,000 cm^3. Therefore, the volume of the rectangular solid is 10.
13.
A bottle of vitamin C contains 100 tablets and weighs 80 g. If the bottle alone weighs 23 g. If the bottle alone weighs 23 g
What is the mass of a tablet ( in g)?
Correct Answer
B. .75
Explanation
The mass of the bottle alone is 23 g. Therefore, the total mass of the bottle and the tablets is 80 g. To find the mass of a tablet, we subtract the mass of the bottle from the total mass. So, 80 g - 23 g = 57 g. Since there are 100 tablets in the bottle, we divide the total mass of the tablets (57 g) by the number of tablets (100) to find the mass of a single tablet. 57 g / 100 = 0.57 g. Therefore, the mass of a tablet is 0.57 g.
14.
A pad of paper (100 leaves) has a mass of 150 g and a total thickness of 1 cm
Find the thickness of a sheet of paper in cm.
0.01 cm
1.5 cm
0.015 cm
3 cm
Correct Answer
A. 0.01 cm
Explanation
Each sheet of paper in the pad has a thickness of 0.01 cm. This can be calculated by dividing the total thickness of 1 cm by the number of sheets in the pad, which is 100. So, each sheet of paper is 0.01 cm thick.
15.
One inch is equal to 2.54 cm; one feet is 12 inches; one yard is three feet. How many centimeters are in one yard?
32.5
57.6
91.44
134.2
Correct Answer
C. 91.44
Explanation
One yard is equal to three feet, and one foot is equal to 12 inches. Therefore, to find the number of centimeters in one yard, we need to convert inches to centimeters. Since one inch is equal to 2.54 cm, 12 inches (one foot) is equal to 30.48 cm. And since one yard is three feet, we multiply 30.48 cm by 3, which gives us 91.44 cm. Therefore, the correct answer is 91.44 cm.