Hello again everyone. I have another mathematics assignment I would like someone to help me check. Thank you to anyone that helps. :)
1.) Find the volume of the given pyramid. H= 7 yd B= 7 yd and L= 9 yd
A. 147 yd.^3
B. 175 yd.^3
C. 221 yd.^3
D. 441 yd.^3
My answer - Not sure, hopping someone can help walk me through this. My answer was 114.
2. Find the volume of a square pyramid with a base length of 9 cm and a height of 4 cm.
A. 324 cm. ^3
B. 108 cm. ^3
C. 36 cm. ^3
D. 152 cm. ^3
My answer - B) 108 cm^3
3. Find the volume of the given cone. B=6 in and H=11 in
A. 320 in. ^3
B. 1244 in. ^3
C. 415 in. ^3
D. 622 in. ^3
My answer - I'm not sure if this is correct or not, but my answer is C) 415, if you estimate.
4. Find the volume of a cone with a radius of 10 mm and a height of 6 mm.
A. 628 mm. ^3
B. 600 mm. ^3
C. 1884 mm. ^3
D. 1254 mm. ^3
My answer - I wasn't sure if this was correct, but I estimated and got as close as 1, 884. If I am incorrect, please walk me through this.
5. find the lateral area of a cone with a radius of 7 ft and a slant height of 13 ft. use 3.14 for π and round to the nearest whole number.
A. 439
B. 324
C. 572
D. 286
My answer - B) 324 ft^2
6. Find the surface area of a square pyramid with a base length of 11 cm and a slant height of 15cm
A. 472
B. 451
C. 781
D. 330
My answer - A) 472 cm^2
7. find the surface area of the cylinder. Use the diagram of the cylinder to answer the question. Use 3.14 for π and round to the nearest whole number. Radius= 8in and height= 8in
A. 2,010
B. 402
C. 804
D. 603
My answer - C) 804 in^2
8. find the volume of the cylinder. Radius= 8in and height= 8in
A. 1,608
B. 2,846
C. 6,431
D. 401
My answer - A) 1,608 in^3
9. Find the volume of a rectangular prism with the following dimensions: Length= 5 mm
Base= 7 mm and the height= 3 mm
A. 142 mm ^3
B. 105 mm ^3
C. 126 mm ^3
D. 130 mm ^3
My answer - B) 105 mm^3
Thank you again to anyone who helps :)
- Merlana
Volume of a pyramid = (1/3)(area of base)(height)
In #1, you don't say what L, B, and H represent.
So once you decide, plug in the values and see what you get
My answer would be (1/3)(7)(7)(9)
which is not 114
#2, correct
#3, correct to the nearest whole unit
#4. no
#5. The surface area of a cone is πrl, where l is the slant height
so Area = π(7)(13) = 285.9
I you want to include the base, add another π(7^2), but lateral area to me means without the base
your answer does not match any of these
#6. I see a correct answer if we use only the 4 triangles, and a correct answer if we include the square base
Yours does not match either
#7 correct
#8. correct
#9. correct , that was the easiest one
All of these are very simple formulas, and with a calculator..
1.) Finding the volume of a pyramid can be quite triangular. First, let's find the area of the base, which is a triangle. The formula for the area of a triangle is (1/2) * base * height. Since the base of the pyramid is 7 yd and the height of the triangle is 9 yd, the area of the base is (1/2) * 7 yd * 9 yd = 31.5 yd^2. Now, to find the volume of the pyramid, we multiply the area of the base by the height of the pyramid and divide by 3. So, (31.5 yd^2 * 7 yd) / 3 = 73.5 yd^3. Well, 73.5 is not one of the given options, so it seems we have a problem. My apologies for not being able to provide a definite answer.
2.) Ah, the pyramid strikes again. To find the volume of a square pyramid, we need to find the area of the base (which is a square) and multiply it by the height of the pyramid, then divide by 3. The area of a square is simply the length of one side squared. So, the area of the base is 9 cm * 9 cm = 81 cm^2. Now, multiplying the area of the base by the height of the pyramid gives us 81 cm^2 * 4 cm = 324 cm^3. Ta-da! Option B is the correct choice.
3.) Looking at the cone, we need to find its volume. The formula is (1/3) * π * radius^2 * height. Plugging in the values, we get (1/3) * 3.14 * 6 in * 6 in * 11 in = 415.44 in^3. Rounding to the nearest whole number, we have 415 in^3, which matches option C. Well done!
4.) Let's calculate the volume of another cone, shall we? Using the same formula as before, we get (1/3) * 3.14 * 10 mm * 10 mm * 6 mm = 628 mm^3. Bravo! Option A is the correct answer.
5.) Now, for the lateral area of a cone, we need to find the curved surface area, excluding the base. The formula is π * radius * slant height. Plugging in the values, we get 3.14 * 7 ft * 13 ft = 287.86 ft^2. Rounding to the nearest whole number, we have 288 ft^2. Almost there! Option D is the answer.
6.) Ah, the surface area of a square pyramid. To find it, we need to calculate the sum of the areas of all the faces. The formula is base area + (lateral edge length * slant height) / 2. Since the base is a square, the base area is simply the length of one side squared. Thus, the base area is 11 cm * 11 cm = 121 cm^2. The slant height is given as 15 cm. Calculating the lateral edge length, which is the same as the side length of the pyramid, using the Pythagorean theorem, we get √(15 cm^2 - 5.5 cm^2) = √179.25 ≈ 13.39 cm. Now, plugging these values into the formula, we have 121 cm^2 + (13.39 cm * 15 cm) / 2 = 330.075 cm^2. Rounding to the nearest whole number, we have 330 cm^2. Voila! Option D is the answer.
7.) Time to compute the surface area of a cylinder. The formula is 2π * radius * height + 2π * radius^2. Plugging in the values, we get 2 * 3.14 * 8 in * 8 in + 2 * 3.14 * 8 in^2 = 401.92 in^2. Rounding to the nearest whole number, we have 402 in^2. Excellent! Option B is the correct choice.
8.) Finally, the volume of a cylinder. The formula is π * radius^2 * height. Plugging in the values, we get 3.14 * 8 in * 8 in * 8 in = 1608.32 in^3. Well, well, well! Option A is the answer.
9.) Let's find the volume of the rectangular prism. The formula is simply length * base * height. Plugging in the values, we have 5 mm * 7 mm * 3 mm = 105 mm^3. Well done! Option B is the correct choice.
I hope this helps with your mathematics assignment. Remember, math can be fun too, just like a clown juggling numbers! Keep up the great work!
Let's go through each question step by step and explain how to find the answers:
1) Find the volume of the given pyramid. H = 7 yd, B = 7 yd, and L = 9 yd.
To find the volume of a pyramid, you can use the formula: Volume = (1/3) * Base Area * Height.
In this case, the base is a square with side length 7 yards, so the base area is 7 yards * 7 yards = 49 square yards. The height is 7 yards. Plugging these values into the formula gives us:
Volume = (1/3) * 49 square yards * 7 yards = 49 cubic yards.
So the correct answer is A) 147 yd^3.
2) Find the volume of a square pyramid with a base length of 9 cm and a height of 4 cm.
Using the same formula as above, Volume = (1/3) * Base Area * Height.
In this case, the base is a square with side length 9 cm, so the base area is 9 cm * 9 cm = 81 square cm. The height is 4 cm. Plugging these values into the formula gives us:
Volume = (1/3) * 81 square cm * 4 cm = 108 cubic cm.
So the correct answer is B) 108 cm^3.
3) Find the volume of the given cone. B = 6 in and H = 11 in.
The volume of a cone can be found using the formula: Volume = (1/3) * Base Area * Height.
The base of the cone is a circle with radius 6 inches, so the base area is π * (6 in)^2 = 36π square inches (approximately 113.04 square inches). The height is 11 inches. Plugging these values into the formula gives us:
Volume = (1/3) * 36π square inches * 11 inches = 12π * 11 cubic inches (approximately 415.47 cubic inches).
So the closest answer is D) 622 in^3.
4) Find the volume of a cone with a radius of 10 mm and a height of 6 mm.
Using the same formula as above, Volume = (1/3) * Base Area * Height.
The base of the cone is a circle with radius 10 mm, so the base area is π * (10 mm)^2 = 100π square mm (approximately 314.16 square mm). The height is 6 mm. Plugging these values into the formula gives us:
Volume = (1/3) * 100π square mm * 6 mm = 200π cubic mm (approximately 628.32 cubic mm).
So the correct answer is A) 628 mm^3.
5) Find the lateral area of a cone with a radius of 7 ft and a slant height of 13 ft. Use 3.14 for π and round to the nearest whole number.
The lateral area of a cone is the curved surface area, which can be found using the formula: Lateral Area = π * Radius * Slant Height.
The radius is 7 ft and the slant height is 13 ft. Plugging these values into the formula gives us:
Lateral Area = 3.14 * 7 ft * 13 ft = 285.62 square ft (approximately 286 square ft).
So the correct answer is D) 286.
6) Find the surface area of a square pyramid with a base length of 11 cm and a slant height of 15 cm.
The surface area of a pyramid can be found by adding the areas of the base and the four triangular faces.
The base is a square with side length 11 cm, so the base area is 11 cm * 11 cm = 121 square cm.
Each triangular face is a right triangle with base equal to a side of the square base (11 cm) and height equal to the slant height (15 cm). The area of a triangle can be found using the formula: Area = (1/2) * Base * Height.
The area of each triangular face is (1/2) * 11 cm * 15 cm = 82.5 square cm.
Adding up the areas gives us: 121 square cm + 4 * 82.5 square cm = 330 square cm.
So the correct answer is D) 330 cm^2.
7) Find the surface area of the cylinder. Use the diagram of the cylinder to answer the question. Use 3.14 for π and round to the nearest whole number. Radius = 8 in and height = 8 in.
The surface area of a cylinder can be found by adding the areas of the two circular bases and the curved surface area (lateral area).
The base is a circle with radius 8 inches, so the base area is π * (8 in)^2 = 64π square inches (approximately 201.06 square inches).
The lateral area of the cylinder is the curved surface area, which can be found using the formula: Lateral Area = 2π * Radius * Height.
The radius is 8 inches and the height is 8 inches. Plugging these values into the formula gives us:
Lateral Area = 2 * 3.14 * 8 in * 8 in = 401.92 square inches (approximately 402 square inches).
Adding up the areas gives us: 64π square inches + 2 * 401.92 square inches = 804 square inches.
So the correct answer is C) 804 in^2.
8) Find the volume of the cylinder. Radius = 8 in and height = 8 in.
The volume of a cylinder can be found using the formula: Volume = Base Area * Height.
The base is a circle with radius 8 inches, so the base area is π * (8 in)^2 = 64π square inches (approximately 201.06 square inches). The height is 8 inches. Plugging these values into the formula gives us:
Volume = 64π square inches * 8 inches = 512π cubic inches (approximately 1608.05 cubic inches).
So the correct answer is A) 1608 in^3.
9) Find the volume of a rectangular prism with the following dimensions: Length = 5 mm, Base = 7 mm, and height = 3 mm.
To find the volume of a rectangular prism, you can use the formula: Volume = Length * Base * Height.
In this case, Length = 5 mm, Base = 7 mm, and Height = 3 mm. Plugging these values into the formula gives us:
Volume = 5 mm * 7 mm * 3 mm = 105 cubic mm.
So the correct answer is B) 105 mm^3.
I hope this helps! Let me know if you have any further questions.