Praticando Um Pouco Mais - 9º Ano - 3ª Etapa

Explanation
The shaded region is formed by subtracting the area of the square from the area of the sector of the circle. The area of the square is found by multiplying the length of one side by itself, so it is 2 cm x 2 cm = 4 cm². The sector of the circle is a fraction of the whole circle, and its angle is 90 degrees (since it is a quadrant). The formula to calculate the area of a sector is (angle/360) x πr², where r is the radius of the circle. In this case, the radius is 2 cm, so the area of the sector is (90/360) x π x 2² = 1/4 x π x 4 = π cm². Subtracting the area of the square from the area of the sector gives us the shaded area: π cm² - 4 cm² = (π - 4) cm².

Explanation
The area of the rectangle ABCD can be found by multiplying the length and width of the rectangle. Since the width of each rectangular plank is given as 10 cm, the length of the rectangle can be found by calculating the circumference of the circle. The circumference of a circle is given by the formula 2πr, where r is the radius of the circle. In this case, the radius is equal to half the width of the plank, which is 5 cm. Therefore, the circumference is 2π(5) = 10π cm. The length of the rectangle is equal to the circumference, which is 10π cm. Multiplying the length and width, we get 10π * 10 = 100π cm². To find the area in cm², we need to approximate the value of π to 3.14. Therefore, the area is approximately 100 * 3.14 = 314 cm². However, since the answer choices are in whole numbers, we need to find the closest whole number to 314, which is 300. Therefore, the correct answer is 1600.

Explanation
When the edge of a cube is increased by 1 cm, the volume of the cube increases by the product of the increase in the edge length and the area of the base. In this case, the increase in the edge length is 1 cm, and the area of the base is 10 cm * 10 cm = 100 cm^2. Therefore, the volume increase is 1 cm * 100 cm^2 = 100 cm^3. Adding this to the original volume of the cube (10 cm * 10 cm * 10 cm = 1000 cm^3) gives a total volume of 1100 cm^3. Thus, the correct answer is 331 cm^3.

Explanation
The given options represent the roots of a quadratic equation. The question asks for the largest root among these options. Among the given options, the largest root is -0.5.

Explanation
The figure shows a right triangle with a square inscribed inside it. The sides of the square are parallel to the legs of the triangle. Since the sides of the square are parallel to the legs of the triangle, they are also perpendicular to the hypotenuse of the triangle. This means that the sides of the square are also the altitude of the right triangle. The altitude divides the right triangle into two smaller similar triangles. According to the similarity of triangles, the ratio of the sides of the smaller triangle to the corresponding sides of the larger triangle is the same. Therefore, the side of the square is equal to the altitude of the right triangle, which is 4.

Explanation
The height of the "pau de sebo" can be determined using the concept of similar triangles. The length of the shadow of the mast is 25 dm, which is equivalent to 2.5 m. The length of the shadow of the "pau de sebo" is 125 dm, which is equivalent to 12.5 m. Since the lengths of the shadows are proportional to the heights of the objects, the height of the "pau de sebo" can be found by setting up the following proportion: 1m/2.5m = x/12.5m. Solving for x gives x = 5m. Therefore, the height of the "pau de sebo" is 5.0 meters.

Explanation
A pilha circular formada pela mangueira de jardim tem um diâmetro de aproximadamente 100 cm, o que significa que o raio da pilha é de 50 cm. O comprimento de uma volta completa da mangueira é igual ao comprimento da circunferência da pilha, que é dado por C = 2πr, onde r é o raio da pilha. Portanto, o comprimento de uma volta completa é aproximadamente 100π cm. Como há seis voltas completas, o comprimento total da mangueira é aproximadamente 600π cm. Para converter esse comprimento para metros, basta dividir por 100, já que 1 metro é igual a 100 centímetros. Portanto, o comprimento da mangueira é aproximadamente 6π metros, o que é aproximadamente igual a 18,85 metros. A resposta mais próxima é 19m.