Ulangan Harian Matematika "Lingkaran" Kelas 8 Unggulan Smp Negeri 1 Sepulu

1. Suatu lingkaran berjari jari r dan mempunyai luas L, maka hubungan antara L dan r berikut yang benar ........

L = r²/π

L =π x r²

r²= 1/π

r²= π x L

The correct answer is L = π x r². This is the correct formula for calculating the area of a circle, where L represents the area and r represents the radius. The formula states that the area of a circle is equal to pi multiplied by the square of the radius.

Explanation

The correct answer is L = π x r². This is the correct formula for calculating the area of a circle, where L represents the area and r represents the radius. The formula states that the area of a circle is equal to pi multiplied by the square of the radius.

2.

pada gambar tersebut yang merupakan tali busur terpanjang adalah ......

EF

DC

FC

DE

The correct answer is FC because in the given options, FC is the longest arc. The length of an arc is determined by the angle it subtends at the center of the circle. In this case, FC subtends a larger angle compared to the other options, resulting in a longer arc. Therefore, FC is the longest arc among the given options.

Explanation

The correct answer is FC because in the given options, FC is the longest arc. The length of an arc is determined by the angle it subtends at the center of the circle. In this case, FC subtends a larger angle compared to the other options, resulting in a longer arc. Therefore, FC is the longest arc among the given options.

3. Juring lingkaran dibatasi oleh 2 jari jari dan ......

1 apotema

diameter

busur yang di apit 2 jari jari

sebuah temberang

The correct answer is "busur yang di apit 2 jari jari". This answer is correct because when we talk about a circle, the arc that is enclosed by two radii is commonly referred to as a sector. The sector is defined by the central angle between the two radii and the length of the arc. Therefore, the busur yang di apit 2 jari jari refers to the arc that is enclosed by two radii in a circle.

Explanation

The correct answer is "busur yang di apit 2 jari jari". This answer is correct because when we talk about a circle, the arc that is enclosed by two radii is commonly referred to as a sector. The sector is defined by the central angle between the two radii and the length of the arc. Therefore, the busur yang di apit 2 jari jari refers to the arc that is enclosed by two radii in a circle.

4. Jika Keliling Sebuah roda sepeda adalah K dan roda sepeda berputar sebanyak N kali, maka panjang lintasan yang dialalui roda sepeda adalah .....

K x N

N : K

K : N

K x N ²

The question states that the circumference of a bicycle wheel is K and the wheel rotates N times. The question is asking for the length of the path traveled by the bicycle wheel. The correct answer is K x N, which means that the length of the path is equal to the circumference of the wheel multiplied by the number of rotations.

Explanation

The question states that the circumference of a bicycle wheel is K and the wheel rotates N times. The question is asking for the length of the path traveled by the bicycle wheel. The correct answer is K x N, which means that the length of the path is equal to the circumference of the wheel multiplied by the number of rotations.

5. Jumlah sudut-sudut yang berhadapan pada segi empat tali busur sama dengan........˚

90

120

180

360

The sum of opposite angles in a quadrilateral is always equal to 180 degrees. This is a well-known property of quadrilaterals. Therefore, the correct answer is 180 degrees.

Explanation

The sum of opposite angles in a quadrilateral is always equal to 180 degrees. This is a well-known property of quadrilaterals. Therefore, the correct answer is 180 degrees.

6.

dari gambar tersebut besar < AOB = 80˚ maka besar <ACB adalah .....

20˚

40˚

60˚

160˚

From the given information, it is stated that the angle AOB is 80 degrees. The angle ACB is formed by the line segments AC and CB. Since the angle AOB is given, we can conclude that angle ACB is the supplementary angle to AOB. The sum of supplementary angles is always 180 degrees. Therefore, angle ACB is 180 - 80 = 100 degrees. However, none of the given answer choices match this value. Hence, an explanation for the correct answer is not available.

Explanation

From the given information, it is stated that the angle AOB is 80 degrees. The angle ACB is formed by the line segments AC and CB. Since the angle AOB is given, we can conclude that angle ACB is the supplementary angle to AOB. The sum of supplementary angles is always 180 degrees. Therefore, angle ACB is 180 - 80 = 100 degrees. However, none of the given answer choices match this value. Hence, an explanation for the correct answer is not available.

7. Tali busur yang melalui titik pusat lingkaran disebut........

jari-jari

apotema

diameter

tembereng

The correct answer is "diameter". The diameter of a circle is a line segment that passes through the center of the circle and has both endpoints on the circle. In this question, it is mentioned that the bowstring passes through the center of the circle, which is a characteristic of the diameter. Therefore, the correct term for a bowstring passing through the center of a circle is "diameter".

Explanation

The correct answer is "diameter". The diameter of a circle is a line segment that passes through the center of the circle and has both endpoints on the circle. In this question, it is mentioned that the bowstring passes through the center of the circle, which is a characteristic of the diameter. Therefore, the correct term for a bowstring passing through the center of a circle is "diameter".

8.

Pada gambar tersebut diketahui besar sudut PRQ = 50 derajat , maka besar sudut POQ adalah ....

150˚

100˚

75˚

25˚

The angle POQ is the supplementary angle to angle PRQ. Since angle PRQ is given as 50 degrees, the supplementary angle to 50 degrees is 180 degrees - 50 degrees = 130 degrees. However, the angle POQ is half of the supplementary angle, so it would be 130 degrees / 2 = 65 degrees. Therefore, the correct answer is 65 degrees.

Explanation

The angle POQ is the supplementary angle to angle PRQ. Since angle PRQ is given as 50 degrees, the supplementary angle to 50 degrees is 180 degrees - 50 degrees = 130 degrees. However, the angle POQ is half of the supplementary angle, so it would be 130 degrees / 2 = 65 degrees. Therefore, the correct answer is 65 degrees.

9. Sudut pusat dibatasi oleh ......

1 busur dan 1 jari jari

2 jari jari

2 jari jari dan 1 busur yang diapitnya

2 busur dan 1 jari jari

The correct answer is "2 jari jari dan 1 busur yang diapitnya." This is because the central angle is formed by two radii of the circle and the arc that is enclosed by these radii. The radii extend from the center of the circle to the endpoints of the arc, and the central angle is the angle formed by these radii. Therefore, the central angle is defined by two radii and the arc that is enclosed by them.

Explanation

The correct answer is "2 jari jari dan 1 busur yang diapitnya." This is because the central angle is formed by two radii of the circle and the arc that is enclosed by these radii. The radii extend from the center of the circle to the endpoints of the arc, and the central angle is the angle formed by these radii. Therefore, the central angle is defined by two radii and the arc that is enclosed by them.

10.

dari gambar tersebut titik O adalah titik pusat lingkaran, pernyataan berikut yang benar adalah .....

< AOB =< ACB

< ADB = 2x < AOB

< ACB = 2x < AOB

< ADB + < ACB = < AOB

The given answer states that the sum of angles ADB and ACB is equal to angle AOB. This is because angle AOB is the central angle of the circle, and angles ADB and ACB are inscribed angles that intercept the same arc. According to the inscribed angle theorem, the measure of an inscribed angle is half the measure of its intercepted arc. Therefore, angle ADB is equal to half of angle AOB, and angle ACB is also equal to half of angle AOB. Adding these two angles together gives us the sum of ADB and ACB, which is equal to angle AOB.

Explanation

The given answer states that the sum of angles ADB and ACB is equal to angle AOB. This is because angle AOB is the central angle of the circle, and angles ADB and ACB are inscribed angles that intercept the same arc. According to the inscribed angle theorem, the measure of an inscribed angle is half the measure of its intercepted arc. Therefore, angle ADB is equal to half of angle AOB, and angle ACB is also equal to half of angle AOB. Adding these two angles together gives us the sum of ADB and ACB, which is equal to angle AOB.

11. Jarak tali busur yang titik pusat lingkaran disebut sebagai ......

jari jari

diameter

tembereng

apotema

The distance from the center of a circle to the chord is called the apothem.

Explanation

The distance from the center of a circle to the chord is called the apothem.

12.

Pada gambar tersebut panjang busur AB = 5 cm, panjang busur CD =8 cm, dan sudut AOB = 15 derajat, maka besar sudut COD adalah ......

24˚

30˚

25˚

36˚

The angle COD can be found by using the formula for the length of an arc: L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the angle subtended by the arc at the center of the circle. In this case, we are given the lengths of the arcs AB and CD, as well as the angle AOB. We can set up the equation 5 = r * 15° and solve for the radius r. Then, we can use the equation 8 = r * θ to solve for θ, which gives us θ = 24°. Therefore, the angle COD is 24°.

Explanation

The angle COD can be found by using the formula for the length of an arc: L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the angle subtended by the arc at the center of the circle. In this case, we are given the lengths of the arcs AB and CD, as well as the angle AOB. We can set up the equation 5 = r * 15° and solve for the radius r. Then, we can use the equation 8 = r * θ to solve for θ, which gives us θ = 24°. Therefore, the angle COD is 24°.

13. Sebuah lingkaran mempunyai jari-jari 14 cm maka pernyataan yang benar adalah .....

diameter = 28cm

Keliling = 88cm

Luas = 154 cm²

a,b benar

The statement "a,b benar" means that both statements a and b are correct. In this case, statement a is that the diameter of the circle is 28 cm, which is correct because the diameter is always twice the length of the radius. Statement b is that the circumference of the circle is 88 cm, which is also correct because the circumference can be calculated using the formula C = 2πr, where r is the radius. Therefore, both statements are true.

Explanation

The statement "a,b benar" means that both statements a and b are correct. In this case, statement a is that the diameter of the circle is 28 cm, which is correct because the diameter is always twice the length of the radius. Statement b is that the circumference of the circle is 88 cm, which is also correct because the circumference can be calculated using the formula C = 2πr, where r is the radius. Therefore, both statements are true.

14.

luas daerah yang di arsir pada gambar tersebut adalah ....

154 cm²

308 cm²

616 cm²

77 cm²

The correct answer is 308 cm².

Explanation

The correct answer is 308 cm².

15.

Jika L adalah pusat lingkaran maka daerah yang di arsir pada gambar disebut .........

tembereng

juring

tembereng dan juring

busur

The correct answer is "tembereng dan juring". The question is asking for the name of the shaded area in the given image if L is the center of the circle. A "tembereng" is a segment of a circle bounded by a chord and an arc, while a "juring" is a sector of a circle bounded by an arc and two radii. Therefore, the shaded area in the image can be referred to as both a "tembereng" and a "juring".

Explanation

The correct answer is "tembereng dan juring". The question is asking for the name of the shaded area in the given image if L is the center of the circle. A "tembereng" is a segment of a circle bounded by a chord and an arc, while a "juring" is a sector of a circle bounded by an arc and two radii. Therefore, the shaded area in the image can be referred to as both a "tembereng" and a "juring".