Uji Coba Unbk Matematika

Explanation
The given question asks for the area of the sector AOB, which is a portion of the circle with center O and radius AO. To find the area of a sector, we use the formula A = (θ/360)πr², where θ is the central angle in degrees and r is the radius of the circle. In this case, the central angle AOB is given as 300 degrees and the radius AO is given as 20 cm. Plugging these values into the formula, we get A = (300/360)π(20)² = (5/6)π(400) = (200/3)π ≈ 209.44 cm². Rounding to two decimal places, the area of the sector AOB is approximately 208.67 cm².

Explanation
The probability of two dice showing a total of ten can be found by listing all the possible outcomes. There are 36 possible outcomes when two dice are rolled (6 possible outcomes for the first die and 6 possible outcomes for the second die). Out of these 36 outcomes, there are 3 outcomes where the total is ten (4+6, 5+5, 6+4). Therefore, the probability of getting a total of ten is 3/36, which simplifies to 1/12.

Explanation
Based on the given information, we can see that AB is 13 cm and AD is 9 cm. To find the length of CD, we can use the Pythagorean theorem. CD is the hypotenuse of the right triangle ACD, with AD and AC as the other two sides. Using the Pythagorean theorem, we can calculate the length of AC.

AC^2 = AB^2 - BC^2
AC^2 = 13^2 - 9^2
AC^2 = 169 - 81
AC^2 = 88

Taking the square root of both sides, we find that AC is approximately 9.38 cm. Therefore, the length of CD is approximately 6 cm.

Explanation
The length of EF is 7 cm because in congruent triangles, corresponding sides are equal in length. Therefore, if triangle ABC is congruent to triangle DEF, the length of side EF must be equal to the length of side BC, which is 7 cm.

Explanation
Based on the given information, we can use the concept of similar triangles to find the height of the building. The ratio of the height of the building to the length of its shadow is equal to the ratio of the height of the student to the length of their shadow.

So, we can set up the proportion:
height of building / length of shadow of building = height of student / length of student's shadow

Let x be the height of the building.
Therefore, we can write the proportion as:
x / 56 = 1.5 / 3.5

Cross-multiplying, we get:
3.5x = 56 * 1.5
3.5x = 84
x = 84 / 3.5
x ≈ 24

Hence, the height of the building is approximately 24 meters.

Explanation
A prism with an octagonal base has 10 sides.

Explanation
The given image shows a cube with numbered squares. If square number 1 is the bottom side of the cube, the square number 6 is the top side of the cube.

Explanation
The prism has a rhombus-shaped base with diagonal lengths of 12 cm and 16 cm. The total surface area of the prism is given as 392 cm2. To find the volume of the prism, we need to find the height. We can use the formula for the surface area of a prism: 2(base area) + (perimeter of base) * height. Since the base is a rhombus, the base area is (1/2) * (12 cm) * (16 cm) = 96 cm2. The perimeter of the base is 4 * (12 cm + 16 cm) = 112 cm. Plugging these values into the formula, we get 2(96 cm2) + (112 cm)(height) = 392 cm2. Solving for the height, we get height = (392 cm2 - 2(96 cm2)) / (112 cm) = 2 cm. Finally, we can find the volume of the prism using the formula: volume = (base area) * height = (96 cm2) * (2 cm) = 192 cm3. Therefore, the correct answer is 480 cm3.

Explanation
The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius of the base, and h is the height of the cylinder. In this case, the radius (r) is given as 14 cm and the height (h) is given as 10 cm. Plugging these values into the formula, we get V = (22/7)(14^2)(10) = 8,909.33 cm3. Therefore, the correct answer is 8,909.33 cm3.

Explanation
The correct answer is 2.200 cm2. To find the surface area of the cone, we need to calculate the curved surface area and the base area separately. The curved surface area can be found using the formula πrℓ, where r is the radius of the base and ℓ is the slant height of the cone. The radius is half of the diameter, so r = 28/2 = 14 cm. To find ℓ, we can use the Pythagorean theorem, where ℓ^2 = h^2 + r^2. Given that the height is 48 cm, we can calculate ℓ as ℓ = √(48^2 + 14^2) ≈ 50.92 cm. Therefore, the curved surface area is π * 14 * 50.92 ≈ 2,200 cm2. The base area can be found using the formula πr^2, which is π * 14^2 = 616 cm2. Adding the curved surface area and the base area together, we get a total surface area of 2,200 cm2.

Explanation
The correct answer is 10 orang. This means that there are 10 students who have a weight less than the average weight.

Explanation
The average of the first six students is 70. When the seventh and eighth students take a makeup test and get a score of 80, it will increase the overall average. Since the makeup test scores are higher than the average, the new average will be closer to 80 than 70. Therefore, the most reasonable option is 72.5, as it is the closest to 80 while still being higher than the original average of 70.

Explanation
Based on the given diagram, the circle representing the background education of the parents is divided into four sections. Since the total number of parents is 900, each section represents a certain percentage of the total. To determine the number of parents with a background in junior high school (SMP), we need to find the section that represents this category. The section that corresponds to 324 parents is the one labeled SMP, indicating that 324 parents have a background in junior high school. Therefore, the correct answer is 324 orang.

Explanation
The participant answered 8 questions correctly, which gives them a score of 8 x 20 = 160. They did not answer 3 questions, which means they did not receive any points for those. Therefore, the total score they obtained is 160.

Explanation
If a gallon can fill 40 small glasses and 20 large glasses, then the total volume of water in the gallon can be calculated by multiplying the volume of one small glass by the number of small glasses and the volume of one large glass by the number of large glasses.

The volume of one small glass is 1/4 liter, so the total volume of water in the small glasses is (1/4) * 40 = 10 liters.

The volume of one large glass is 2/5 liter, so the total volume of water in the large glasses is (2/5) * 20 = 8 liters.

Therefore, the total volume of water in the gallon is 10 liters + 8 liters = 18 liters.

Explanation
The project was initially planned to be completed in 25 days by 6 workers. However, on day 9, the project was suspended for 4 days. This means that the project lost 4 days of work. To make up for this lost time and ensure that the project is completed on time, an additional 8 workers are needed. With 14 workers in total, the project can be completed within the original 25-day timeframe.