1.
In a triangle ABC, the length of the side AB is 6 cm.
The length of the side BC is 8 cm.
The angle A is 60 degree.
Find the length AC.
Correct Answer
B. 9.08 cm
Explanation
Using the Law of Cosines, we can find the length of AC. The formula is given by AC^2 = AB^2 + BC^2 - 2*AB*BC*cos(A), where A is the angle opposite to side AC. Plugging in the given values, we get AC^2 = 6^2 + 8^2 - 2*6*8*cos(60). Simplifying, AC^2 = 36 + 64 - 96*cos(60). Since cos(60) = 1/2, AC^2 = 100 - 96/2 = 100 - 48 = 52. Taking the square root of both sides, we get AC â‰ˆ 9.08 cm.
2.
What is the volume of a cube whose surface area is 216 ?
Correct Answer
B. 216
Explanation
The volume of a cube can be found by taking the cube root of the surface area. In this case, the cube root of 216 is 6. Therefore, the volume of the cube is 6^3, which equals 216.
3.
What is the volume of a rectangular prism whose edges measure 2ft, 2ft, and 3ft?
Correct Answer
B. 12 cubic feet
Explanation
The volume of a rectangular prism is found by multiplying the length, width, and height of the prism. In this case, the length is 2ft, the width is 2ft, and the height is 3ft. Multiplying these values together gives us 12 cubic feet.
4.
A cone has a volume of 600TT cubic inches and a height of 50 in. What is the radius of the cone?
Correct Answer
A. 6 in.
Explanation
The volume of a cone is given by the formula V = (1/3)Ï€r^2h, where V is the volume, r is the radius, and h is the height. In this case, the volume is given as 600Ï€ cubic inches and the height is given as 50 inches. Plugging these values into the formula, we get 600Ï€ = (1/3)Ï€r^2(50). Simplifying this equation, we get 600 = (1/3)r^2(50). Dividing both sides by (1/3)(50), we get r^2 = 12. Taking the square root of both sides, we find that r = âˆš12, which is approximately 3.46. Therefore, none of the given answer choices are correct.
5.
A right cylinder has a radius of 6 inches and a height of 8 inches.
Find its surface area and volume?
Correct Answer
C. S.A = 168 TT , V = 288 TT
Explanation
The correct answer is S.A = 168 TT, V = 288 TT. The surface area of a cylinder is given by the formula 2Ï€r(r+h), where r is the radius and h is the height. Plugging in the values, we get 2Ï€(6)(6+8) = 168Ï€ TT. The volume of a cylinder is given by the formula Ï€r^2h. Plugging in the values, we get Ï€(6^2)(8) = 288Ï€ TT. Therefore, the surface area is 168 TT and the volume is 288 TT.
6.
The hexagonal has:
Correct Answer
C. 8 faces
Explanation
The given answer, "8 faces," is incorrect. A hexagonal shape has six sides or faces. Therefore, the correct answer should be "6 faces."
7.
A solid shape has 15 edges and 9 vertices.
How many faces does it have?
Correct Answer
A. 8 faces
Explanation
A solid shape with 15 edges and 9 vertices is most likely a cube. A cube has 6 faces, and each face is made up of 4 edges. Therefore, a cube with 15 edges would have 15/4 = 3.75 faces. Since a face cannot be divided into parts, the number of faces must be a whole number. The closest whole number to 3.75 is 4. However, since a cube has 6 faces, the correct answer is 8 faces.
8.
Find the surface area of a square pyramid with base edges 5 m and a slant height 3 m.
Correct Answer
C. 55 square meter
Explanation
The surface area of a square pyramid can be calculated by finding the area of the base and adding the areas of the four triangular faces. The base of the pyramid is a square with side length 5 m, so its area is 5^2 = 25 square meters. The slant height of the pyramid is 3 m, which is also the height of each triangular face. The area of each triangular face can be calculated using the formula (1/2) * base * height, where the base is the side length of the square base (5 m) and the height is the slant height (3 m). Therefore, the area of each triangular face is (1/2) * 5 * 3 = 7.5 square meters. Since there are four triangular faces, the total area of the triangular faces is 4 * 7.5 = 30 square meters. Adding the area of the base and the triangular faces, we get 25 + 30 = 55 square meters.
9.
The length of the longer leg of a semi-equilateral triangle is 6.92 m.
Find the length of the hypotenuse?
Correct Answer
C. 8 m
Explanation
In a semi-equilateral triangle, two sides are equal in length while the third side is longer. The length of the longer leg is given as 6.92 m. Since the triangle is semi-equilateral, the two equal sides will also be 6.92 m each. The hypotenuse of a right triangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the squares of the two equal sides (6.92 m) will be added together and then the square root will be taken to find the length of the hypotenuse. The calculation results in a length of 8 m for the hypotenuse. Therefore, the correct answer is 8 m.
10.
In a right triangle, the length of the shorter leg is 4 cm, and the length of the longer leg is 6.9cm.
Find the smallest acute angle.
Correct Answer
D. None of the above
11.
The measure lengths of a right triangle are: 11cm, 60cm, and 61cm.
Find the largest acute angle.
Correct Answer
C. 79.61 degrees
Explanation
The largest acute angle in a right triangle is always opposite the longest side, which is the hypotenuse. In this case, the hypotenuse has a length of 61cm. To find the largest acute angle, we can use the sine function. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse. So, sin(angle) = 11cm/61cm. Taking the inverse sine of both sides, we find that the angle is approximately 79.61 degrees.
12.
Find the area of a triangle whose sides lengths are 7, 9, and 12.
Correct Answer
A. 31.3 square unit
Explanation
To find the area of a triangle, we can use Heron's formula. Heron's formula states that the area of a triangle with sides of lengths a, b, and c is equal to the square root of s(s-a)(s-b)(s-c), where s is the semiperimeter of the triangle. In this case, the semiperimeter is (7+9+12)/2 = 14. Using Heron's formula, we can calculate the area as the square root of 14(14-7)(14-9)(14-12) = 31.3 square units. Therefore, the correct answer is 31.3 square units.
13.
In a triangle ABC, the measure angle B is 110 degrees, a = 10cm, and c = 15 cm.
Find b.
Correct Answer
D. None of the above