The length of the car in Megan's scale drawing is 6 cm, and the scale ratio is 3 cm to 2 m.
To find the actual length of the car, we can set up a proportion:
3 cm = 2 m
6 cm = x
Cross multiply to solve for x:
3 * x = 6 * 2
3x = 12
x = 4
So, the actual length of the car is 4 meters.
Now, we can find the length of the car in Ivan's scale drawing. The scale ratio for Ivan is 2 cm to 1 m, so using the actual length of the car (4 meters), we can find the length in Ivan's drawing:
2 cm = 1 m
x cm = 4 m
Cross multiply:
2 * 4 = 1 * x
8 = x
Therefore, the length of the car in Ivan's scale drawing is 8 cm.
Megan creates a scale drawing of a car. The ratio of her scale drawing length to actual car length is 3 cm: 2 m. The length of the car in her drawing is 6 cm.
Ivan draws a scale drawing of the same car. His ratio of scale drawing length to actual car length is 2 cm: 1 m.
What is the length of the car in Ivan's scale drawing?
3 cm
8 cm
12 cm
4 cm
11 answers
A box in the shape of a rectangular prism has a length of 3 5/8 inches, a width of 2 1/2 inches, and a height of 4 inches. What is the volume of the box?
To find the volume of a rectangular prism, you multiply the length, width, and height.
First, convert all the measurements to fractions if necessary.
Length: 3 5/8 = 29/8
Width: 2 1/2 = 5/2
Height: 4
Now, multiply the length, width, and height:
Volume = (29/8) * (5/2) * 4
Volume = (145/16) * 4
Volume = 580/16
Volume = 36 1/4
Therefore, the volume of the box is 36 1/4 cubic inches.
First, convert all the measurements to fractions if necessary.
Length: 3 5/8 = 29/8
Width: 2 1/2 = 5/2
Height: 4
Now, multiply the length, width, and height:
Volume = (29/8) * (5/2) * 4
Volume = (145/16) * 4
Volume = 580/16
Volume = 36 1/4
Therefore, the volume of the box is 36 1/4 cubic inches.
The side lengths of a triangle are 4 inches, 6 inches, and 9 inches. Is this triangle a right triangle? Use the drop-down menus to explain your answer.
Click the arrows to choose an answer from each menu.
The triangle (is not, is) a right triangle because the square of the longest side is (greater than, equal to, less than) the sum of the squares of the shorter sides.
Click the arrows to choose an answer from each menu.
The triangle (is not, is) a right triangle because the square of the longest side is (greater than, equal to, less than) the sum of the squares of the shorter sides.
The triangle (is not) a right triangle because the square of the longest side is (greater than) the sum of the squares of the shorter sides.
Explanation: In a right triangle, the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides (legs), according to the Pythagorean theorem. If the square of the longest side is greater than the sum of the squares of the other two sides, it is not a right triangle. In this case, the square of 9 inches (81) is greater than the sum of the squares of 4 inches (16) and 6 inches (36), which is 52. Therefore, this is not a right triangle.
Explanation: In a right triangle, the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides (legs), according to the Pythagorean theorem. If the square of the longest side is greater than the sum of the squares of the other two sides, it is not a right triangle. In this case, the square of 9 inches (81) is greater than the sum of the squares of 4 inches (16) and 6 inches (36), which is 52. Therefore, this is not a right triangle.
A beach ball has a diameter of 18 inches. What is the approximate volume, rounded to the nearest whole number, of the inflated beach ball? Use
3.14 for pi.
24,417 in. 3
3,052 in.3
1,017 in.'
9,156 in.3
3.14 for pi.
24,417 in. 3
3,052 in.3
1,017 in.'
9,156 in.3
To find the volume of a sphere, you use the formula V = (4/3)πr^3, where r is the radius.
Given that the diameter of the beach ball is 18 inches, the radius would be half of that, which is 9 inches.
Now, substitute the radius into the formula and calculate the volume:
V = (4/3) * 3.14 * 9^3
V ≈ (4/3) * 3.14 * 729
V ≈ 4.19 * 729
V ≈ 3051.51
Rounded to the nearest whole number, the approximate volume of the inflated beach ball is 3,052 in³.
Therefore, the answer is 3,052 in.³.
Given that the diameter of the beach ball is 18 inches, the radius would be half of that, which is 9 inches.
Now, substitute the radius into the formula and calculate the volume:
V = (4/3) * 3.14 * 9^3
V ≈ (4/3) * 3.14 * 729
V ≈ 4.19 * 729
V ≈ 3051.51
Rounded to the nearest whole number, the approximate volume of the inflated beach ball is 3,052 in³.
Therefore, the answer is 3,052 in.³.
This net can be folded to make a square pyramid. What is the surface area of the pyramid?
150 square inches
40 square inches
145 square inches
85 square inches
Height on one side of the triangle: 6
Length on one of the triangle: 5
150 square inches
40 square inches
145 square inches
85 square inches
Height on one side of the triangle: 6
Length on one of the triangle: 5
To find the surface area of a square pyramid, we need to calculate the area of the square base and the areas of the four triangular faces.
Given that the side length of the square base is 5 inches, and the height of each triangular face is 6 inches, we can calculate the surface area as follows:
1. Area of the square base:
The area of the square base = side length squared
The area = 5 * 5 = 25 square inches
2. Area of one triangular face:
The area of a triangle = (1/2) * base * height
The base of the triangle is the side length of the square base, which is 5 inches, and the height of the triangle is 6 inches.
Area of one triangle: (1/2) * 5 * 6 = 15 square inches
Since there are four triangular faces, the total area of the four triangular faces = 4 * 15 = 60 square inches
3. Total surface area of the square pyramid:
Total surface area = area of the square base + area of the four triangular faces
Total surface area = 25 + 60 = 85 square inches
Therefore, the surface area of the square pyramid is 85 square inches.
Given that the side length of the square base is 5 inches, and the height of each triangular face is 6 inches, we can calculate the surface area as follows:
1. Area of the square base:
The area of the square base = side length squared
The area = 5 * 5 = 25 square inches
2. Area of one triangular face:
The area of a triangle = (1/2) * base * height
The base of the triangle is the side length of the square base, which is 5 inches, and the height of the triangle is 6 inches.
Area of one triangle: (1/2) * 5 * 6 = 15 square inches
Since there are four triangular faces, the total area of the four triangular faces = 4 * 15 = 60 square inches
3. Total surface area of the square pyramid:
Total surface area = area of the square base + area of the four triangular faces
Total surface area = 25 + 60 = 85 square inches
Therefore, the surface area of the square pyramid is 85 square inches.
A flower garden is in the shape of a circle. The circumference of the garden is 20 meters.
What is the area of the garden? Use 3.14 for i and round your answer to the nearest whole number.
32 m
40 m
127 m
314 m
What is the area of the garden? Use 3.14 for i and round your answer to the nearest whole number.
32 m
40 m
127 m
314 m
To find the area of the garden, you would first need to calculate the radius of the garden from the given circumference.
Given that the circumference of the garden is 20 meters, you can use the formula for the circumference of a circle: C = 2πr where C is the circumference and r is the radius.
20 = 2 * 3.14 * r
20 = 6.28r
r = 20 / 6.28
r ≈ 3.18 (rounded to two decimal places)
Now that you have the radius, you can calculate the area of the circle using the formula A = πr²:
A = 3.14 * (3.18)²
A ≈ 3.14 * 10.08
A ≈ 31.72
Rounded to the nearest whole number, the area of the garden is 32 square meters.
Therefore, the answer is 32 m².
Given that the circumference of the garden is 20 meters, you can use the formula for the circumference of a circle: C = 2πr where C is the circumference and r is the radius.
20 = 2 * 3.14 * r
20 = 6.28r
r = 20 / 6.28
r ≈ 3.18 (rounded to two decimal places)
Now that you have the radius, you can calculate the area of the circle using the formula A = πr²:
A = 3.14 * (3.18)²
A ≈ 3.14 * 10.08
A ≈ 31.72
Rounded to the nearest whole number, the area of the garden is 32 square meters.
Therefore, the answer is 32 m².
1 answer