Use 3.14 or Start Fraction 22 over 7 End Fraction for pi.
Find the area of the circle.
A circle has a diameter of 24 centimeters.
A.
1,808.64 cm2
B. 452.16 cm2
C.
75.36 cm2
1 / 10
Solution:
Radius of the circle = diameter/2 = 24/2 = 12 cm
Using the formula for area of a circle: A = pi*r^2
A = 3.14*12^2 = 452.16 cm^2
Therefore, the area of the circle is 452.16 cm^2, option B is correct.
Note: Using 22/7 instead of 3.14 would give a slightly different answer of 452.57 cm^2, but for most purposes the approximation of pi to 3.14 is accurate enough.
Use 3.14 or Start Fraction 22 over 7 End Fraction for pi.
Estimate the area of the circle to the nearest square inch.
A circle has radius 14 inches.
A. 88 in.2
B. 62 in.2
C. 616 in.2
2 / 10
Solution:
Using the formula for area of a circle: A = pi*r^2
A = 3.14 * 14^2 = 615.44 in^2
Rounded to the nearest square inch, the estimated area of the circle is 615 in^2, option C is correct.
Use 3.14 or Start Fraction 22 over 7 End Fraction for pi.
What is the area of the circle? Round your answer to the nearest square unit.
A circle has a diameter of 18 millimeters.
A. 254 mm2
B. 324 mm2
C. 1,017 cm2
3 / 10
Solution:
Radius of the circle = diameter/2 = 18/2 = 9 mm
Using the formula for area of a circle: A = pi*r^2
A = 3.14*9^2 = 254.34 mm^2
Rounded to the nearest square unit, the area of the circle is 254 mm^2, option A is correct.
Use 3.14 or Start Fraction 22 over 7 End Fraction for pi.
Estimate the area of the circle.
A circle has a radius of 70 meters.
A.
2,200 m2
B. 15,400 m2
C. 107,800 m2
4 / 10
Solution:
Using the formula for area of a circle: A = pi*r^2
A = 3.14 * 70^2 = 15,386 m^2 (rounded to the nearest square meter)
Therefore, the estimated area of the circle is 15,400 m^2, option B is correct.
Find the surface area of a cube with side length of 4.5 cm.
A. 81 cm2
B. 91.125 cm2
C. 121.5 cm2
Solution:
The surface area of a cube can be found by using the formula: SA = 6s^2, where s is the length of a side.
SA = 6 * 4.5^2 = 6 * 20.25 = 121.5 cm^2
Therefore, the surface area of the cube is 121.5 cm^2, option C is correct.
What is the surface area of the rectangular prism?
A rectangular prism has length of 1.5 millimeters, width of 1.5 millimeters, and height of 8 millimeters.
A. 52.5 mm2
B. 18 cm2
C. 28.5 cm2
6 / 10
5 of 10 Answered
Solution:
The surface area of a rectangular prism can be found by using the formula: SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
SA = 2(1.5*1.5) + 2(1.5*8) + 2(8*1.5) = 3 + 24 + 24 = 51 mm^2 (rounded to the nearest square millimeter)
Therefore, the surface area of the rectangular prism is 51 mm^2, option A is correct.
What is the surface area of the triangular prism?
The front face of a triangular prism is a right triangle with a left height of 3 centimeters, lower width of 4 centimeters, and hypotenuse of 5 centimeters. The lower right edge of the prism is 9 centimeters and connects the triangles.
A. 120 cm2
B. 114 cm2
C. 108 cm2
7 / 10
Solution:
To find the surface area of a prism, we need to find the area of all its faces and add them up.
The front face of the triangular prism is a right triangle with a height of 3 cm and base of 4 cm, so its area is (1/2)*base*height = (1/2)*4*3 = 6 cm^2.
The bottom and top faces of the prism are congruent triangles with base 9 cm and height 4 cm, so each face has area (1/2)*base*height = (1/2)*9*4 = 18 cm^2.
The two side faces of the prism are rectangles with length 9 cm and width 3 cm, so each face has area length*width = 9*3 = 27 cm^2.
Therefore, the total surface area of the prism is:
SA = area of front face + area of bottom face + area of top face + area of two side faces
SA = 6 + 18 + 18 + 27 + 27
SA = 96 cm^2
Therefore, the surface area of the triangular prism is 96 cm^2, which is not one of the answer choices.
What is the volume of the rectangular prism?
A rectangular prism has length of 21.3 millimeters, width of 8 millimeters, and height of 10 millimeters.
A. 170.4 mm3
B. 926.8 mm3
C. 1,704 mm3
Solution:
The volume of a rectangular prism can be found by using the formula: V = lwh, where l is the length, w is the width, and h is the height.
V = 21.3 * 8 * 10 = 1,704 mm^3
Therefore, the volume of the rectangular prism is 1,704 mm^3, option C is correct.
What is the volume of a cube with side lengths of 7.2 in.?
A. 373.248 in.3
B. 311.04 in.3
C. 3,732.48 in.3
Solution:
The volume of a cube can be found by using the formula: V = s^3, where s is the length of a side.
V = 7.2^3 = 373.248 in^3
Therefore, the volume of the cube is 373.248 in^3, option A is correct.
Find the volume of a rectangular prism with the given dimensions.
length = 7.2 ft, width = 15 ft, height = 5 ft
A. 540 ft3
B. 5,400 ft3
C. 438 ft3
Solution:
The volume of a rectangular prism can be found by using the formula: V = lwh, where l is the length, w is the width, and h is the height.
V = 7.2 * 15 * 5 = 540 ft^3
Therefore, the volume of the rectangular prism is 540 ft^3, option A is correct.
i dont understand how yesterday we were on 3.8 and now we are on 4.2 now the system is making me do so many things im so lost and everything has to be dont by 3:30
I am sorry to hear that you are feeling overwhelmed and lost. It can be difficult to keep up with a fast-paced learning or work environment. Remember to take deep breaths and try to stay calm. It might be helpful to break down tasks into smaller steps and prioritize them according to their urgency. Don't hesitate to ask for help or clarification if you are feeling confused about something. It's okay to take breaks and come back to things later if you are feeling overwhelmed. You got this!
Estimate the circumference of the circle with the given radius or diameter. Use 3.14 for pi. Round to the nearest unit.
A circle has a radius of 24 inches.
A. 27 in.
B. 79 in.
C. 1,809 in.
D. 151 in.
1 / 10
Solution:
The formula for circumference of a circle is: C = 2(pi)r
Plugging in the radius of 24 inches and using pi = 3.14, we get:
C = 2(3.14)(24) = 150.72 inches
Rounded to the nearest unit, the estimated circumference of the circle is 151 inches, option D is correct.
Estimate the circumference of a circle with the radius of 4 inches. Use 3.14 for pi. Round to the nearest hundredth.
A. 25.12 in.
B. 12.56 in.
C. 50.24 in.
D. 624.6 in.
Solution:
The formula for circumference of a circle is: C = 2(pi)r
Plugging in the radius of 4 inches and using pi = 3.14, we get:
C = 2(3.14)(4) = 25.12 inches
Rounded to the nearest hundredth, the estimated circumference of the circle is 25.12 inches, option A is correct.
Name the figure.
The bottom face of the solid is a triangle. The three lateral faces are triangles with a shared vertex point at the top of the solid.
A. cone
B. triangular pyramid
C. triangular prism
D. rectangular prism
4 / 10
3 of 10 Answered
The figure is a triangular pyramid.
Find the surface area of the prism (not drawn to scale).
A rectangular prism has length of 13 meters, width of 6 meters, and height of 5 meters.
A. 48 m2
B. 346 m2
C. 780 m2
D. 195 m2
5 / 10
4 of 10 Answered
Solution:
The surface area of a rectangular prism can be found by using the formula: SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
SA = 2(13*6) + 2(13*5) + 2(6*5) = 156 + 130 + 60 = 346 m^2
Therefore, the surface area of the prism is 346 m^2, option B is correct.
Jamilla is building a square sandbox with sides 7 feet long. She wants to put sand 2 feet deep in the box. How much sand should Jamilla order?
A. 98 ft3
B. 14 ft3
C. 49 ft3
D. 16 ft3
Solution:
The volume of a cube can be found by using the formula: V = s^3, where s is the length of a side.
In this case, the sandbox is a cube with side lengths of 7 feet. Jamilla wants to fill it with sand that is 2 feet deep, which means the effective height of the sandbox is 2 feet less than the actual height of 7 feet.
So, the effective height of the sandbox is 7 - 2 = 5 feet.
The volume of sand Jamilla should order is:
V = s^3 - (s-2)^3, where s is the length of a side.
V = 7^3 - (7-2)^3 = 343 - 125 = 218 ft^3
Therefore, Jamilla should order 218 cubic feet of sand, option D is correct.
Maria needs to wrap the box shown below with no overlap of the wrapping paper. How much wrapping paper does she need?
A rectangular prism is shown with length of 8 inches by width of 2 inches by height of 2 inches.
A. 32 in.2
B. 40 in.2
C. 72 in.2
D. 64 in.2
7 / 10
6 of 10 Answered
Solution:
The surface area of a rectangular prism can be found by using the formula: SA = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
SA = 2(8*2) + 2(8*2) + 2(2*2) = 16 + 32 + 8 = 56 in^2
Therefore, Maria needs 56 square inches of wrapping paper, option D is correct.
What is the volume of a rectangular prism that has a base area of 12 cm2 and a height of 8 cm?
A. 12 cm3
B. 96 cm3
C. 768 cm3
D. 8 cm3
Solution:
The volume of a rectangular prism can be found by using the formula: V = Bh, where B is the area of the base and h is the height.
V = 12 cm^2 * 8 cm = 96 cm^3
Therefore, the volume of the rectangular prism is 96 cm^3, option B is correct.
Note: For questions 9 and 10, remember to show all of the steps that you use to solve the problems. Be sure to use the text box where the question mark (?) first appears to show your mathematical work. You can use the comments field to explain your work. Your teacher will review each step of your response to ensure you receive proper credit for your answer.
Estimate the area of the circle. Use Start Fraction 22 over 7 End Fraction for pi.
A circle has a diameter of 28 centimeters.
Solution:
Radius of the circle = diameter/2 = 28/2 = 14 cm
Using the formula for area of a circle: A = pi*r^2
A = (22/7)*14^2 = 616 cm^2 (rounded to the nearest whole number)
Therefore, the estimated area of the circle is 616 cm^2.
What is the volume of the rectangular prism?
A rectangular prism has length of 10.4 millimeters, width of 5 millimeters, and height of 8 millimeters.
Solution:
The volume of a rectangular prism can be found by using the formula: V = lwh, where l is the length, w is the width, and h is the height.
V = 10.4 * 5 * 8 = 416 mm^3
Therefore, the volume of the rectangular prism is 416 mm^3.