1.
Em um cilinro circular reto a área lateral é 54 π cm² e a medida da altura é o triplo da medida do raio da base. Calcule o volume desse cilindro.
Correct Answer
D. 81 π cm³
Explanation
The lateral area of a cylinder is given by the formula 2πrh, where r is the radius of the base and h is the height. In this case, we are given that the lateral area is 54π cm² and the height is three times the radius. Let's assume the radius is r, then the height would be 3r. Plugging these values into the formula, we get 2πr(3r) = 6πr². We are also given that the volume of the cylinder is asked, which is given by the formula V = πr²h. Substituting the values, we get V = πr²(3r) = 3πr³. Therefore, the volume of the cylinder is 81π cm³.
2.
Calcule o volume de um cilindro equilátero cujo raio da base mede 4 cm.
Correct Answer
B. 128 π cm³
Explanation
To calculate the volume of a cylinder, you need to multiply the area of the base (which is π times the square of the radius) by the height of the cylinder. In this case, the radius of the base is given as 4 cm. Therefore, the area of the base is 16π cm². Since the cylinder is equilateral, the height is also 4 cm. Multiplying the area of the base by the height, we get 16π cm² * 4 cm = 64π cm³. Therefore, the correct answer is 128π cm³.
3.
Um cilindro equilátero tem volume V = 16 π cm³. Calcule a altura desse cilindro.
Correct Answer
E. 4 cm
Explanation
The volume of a cylinder can be calculated using the formula V = πr²h, where V is the volume, r is the radius, and h is the height. In this case, the volume is given as 16π cm³. Since the cylinder is equilateral, the radius and height are equal. Therefore, we can rewrite the formula as 16π = πr²h. By canceling out π on both sides, we get 16 = r²h. Since the radius and height are equal, we can substitute r for h, giving us 16 = r²r. Solving for r, we find that r = 2. Therefore, the height of the cylinder is 2 cm.
4.
Um cilindro tem altura 20 cm. Calcule a área lateral e a área total desse cilindro.
Correct Answer
D. 400 π cm²/600 π cm²
Explanation
The correct answer is 400 π cm²/600 π cm². The lateral area of a cylinder is calculated by multiplying the height of the cylinder by the circumference of the base. In this case, the height is 20 cm and the circumference of the base is 2πr, where r is the radius. Therefore, the lateral area is 20 * 2πr = 40πr cm². The total area of a cylinder is calculated by adding the lateral area to the area of the two bases. Since the bases are circles, their area is πr². Therefore, the total area is 40πr + 2πr² = 2πr(20 + r) cm².
5.
A área lateral de um cilindro equilátero é 16 π cm². Calcule a área da base.
Correct Answer
C. 4 π cm²
Explanation
The question asks to calculate the area of the base of an equilateral cylinder. The lateral area of the cylinder is given as 16π cm². The lateral area of a cylinder is equal to the circumference of the base multiplied by the height. Since the cylinder is equilateral, the circumference of the base is equal to the side length of the equilateral base multiplied by π. Therefore, the side length of the equilateral base is 16π / π = 16 cm. The area of an equilateral triangle is (side length)^2 * √3 / 4. So, the area of the base is (16 cm)^2 * √3 / 4 = 4π cm².
6.
Uma secção meridiana de um cilindro equilátero tem 144 π cm² de área. Calcule a área lateral, área total e o volume desse cilindro.
Correct Answer
C. 144 π cm²/216 π cm²/432 π cm³
Explanation
The given answer is the correct answer because it correctly calculates the lateral area, total area, and volume of the equilateral cylinder. The lateral area is 144 π cm², the total area is 216 π cm², and the volume is 432 π cm³.
7.
Um cilindro circular reto re raio da base 5 cm possui uma secção meridiana equivalente a uma de suas bases ( Asm = Ab ). Calcule a área lateral, a área total e o volume desse cilindro.
Correct Answer
B. 25 π cm²/25 π (π+2) cm²/62,5 π cm³
Explanation
The given answer is the correct answer because it provides the correct formulas and calculations for finding the lateral area, total area, and volume of the given cylinder. The formula for the lateral area of a cylinder is given as 2πrh, where r is the radius of the base and h is the height. The formula for the total area is given as 2πr(r+h), and the formula for the volume is given as πr²h. By substituting the given radius of 5 cm into these formulas, the answer correctly calculates the lateral area as 25π cm², the total area as 25π(π+2) cm², and the volume as 62.5π cm³.