Hi, I was just wondering if someone could check my answers!
1. Find the surface area of a sphere with a radius of 8 cm.
A.267.9 cm
B.803.8 cm**
C.2143.6 cm
D201.0 cm
2. Find he surface area of a sphere with a diameter of 12 m.
A. 452.2 m**
B.150.7 m
C.113.0 m
D.904.3 m
3. Find the volume of a sphere with a radius of 4 ft.
A.33.5 ft
B.67.0 ft
C.267.9 ft**
D.803.8 ft
4. For the pair of similar solids, find the value of the variable. (Shown below is two similar cylinders, one with a height of 6 and radius of 15 and another with an unlisted height and a radius of 5)
A.3 cm
B.18 cm
C.16 cm
D.2 cm**
5. For the pair of similar solids, find the value of the variable. (Shown bellow are two similar pyramids, one with an unlisted base measurement and slant height 24 and one with a base measurement of 4 and a slant height of 8.)
A.12 mm**
B.48 mm
C.20 mm
D.3 mm
6. A pyramid had a height of 5 in. and a surface area of 90 in. Find the surface area of a similar pyramid with a height of 10 in. Round to the nearest tenth, if necessary.
A.360 in
B.180 in**
C.22.5 in
D.3.6 in
7. A rectangular prism has a width of 92 ft and a volume of 240 ft. Find the volume of a similar prism with a width of 46 ft. Roud to the nearest tenth, it necessary.
A.30 ft
B.40 ft
C.60 ft
D.120 ft**
I'm rather confident about them but, if I made any mistakes, it would be nice to know!
#6. Area grows as the square of the scale
Since the larger pyramid is 2 times as big, its area is 4 times as big: 360 in^2
#7 Volume changes as the cube of the scale.
1/2 the width, 1/8 the volume: 30 ft^3
The first 5 are all ok (except for the units on some).
Thank you so much!
1. Your choice is off by about 1 cm, but it is the closest choice
2. yes
3. yes, what are you using for π? Most calculators have an good accurate approximation
4. yes
5. yes
6. no, the surface areas are proportional to the squares of their corresponding sides, so
10^2/5^2 = x/90
4 = x/90
x = 360
7. no, the volumes ..... proportional .... to the cubes of their sides, so
92^3/46^3
= 2^3 = 8
So the new volume is 1/8 of 240 or 30 ft
1. To find the surface area of a sphere, you can use the formula: Surface Area = 4πr^2, where r is the radius of the sphere. In this case, the radius is 8 cm. Plugging the value into the formula, you get: Surface Area = 4π(8^2) = 4π(64) = 256π cm^2. To get the approximate value, you can use the approximation π ≈ 3.14. So the surface area is approximately 256 * 3.14 cm^2 = 803.8 cm^2. Therefore, the correct answer is B. 803.8 cm.
2. Similarly, to find the surface area of a sphere with a diameter of 12 m, you can use the same formula: Surface Area = 4πr^2. The diameter is given as 12 m, which means the radius is half of that, so r = 12/2 = 6 m. Plugging the values into the formula, you get: Surface Area = 4π(6^2) = 4π(36) = 144π m^2. Approximating π as 3.14, the surface area is approximately 144 * 3.14 m^2 = 452.2 m^2. Therefore, the correct answer is A. 452.2 m.
3. The formula for the volume of a sphere is: Volume = (4/3)πr^3, where r is the radius of the sphere. Given the radius is 4 ft, you can plug it into the formula: Volume = (4/3)π(4^3) = (4/3)π(64) = 256π/3 ft^3. Approximating π as 3.14, the volume is approximately 256 * 3.14/3 ft^3 = 267.9 ft^3. Therefore, the correct answer is C. 267.9 ft.
4. Since the two cylinders are similar, the ratio of their corresponding heights is the same as the ratio of their corresponding radii. In this case, the ratio of the heights is 6: x, and the ratio of the radii is 15: 5. Simplifying the ratio, you get 6/x = 15/5. Cross-multiplying, you have 5(6) = 15x, which simplifies to 30 = 15x. Dividing both sides by 15, you get x = 30/15 = 2 cm. Therefore, the correct answer is D. 2 cm.
5. Similar to the previous question, since the two pyramids are similar, the ratio of their corresponding base measurements is the same as the ratio of their corresponding slant heights. In this case, the ratio of the base measurements is x: 4, and the ratio of the slant heights is 24: 8. Simplifying the ratio, you have x/4 = 24/8. Cross-multiplying, you get 8x = 24(4), which simplifies to 8x = 96. Dividing both sides by 8, you get x = 96/8 = 12 mm. Therefore, the correct answer is A. 12 mm.
6. The surface area of a pyramid is given by: Surface Area = (base area) + (0.5 × perimeter × slant height). In this case, the base area is not given, so we only need to consider the second part of the formula. For the first pyramid, the height is 5 in and the surface area is 90 in. Plugging these values into the formula: 90 = 0.5 × perimeter × 5. Rearranging the formula, you have perimeter = 90/(0.5 × 5) = 90/2.5 = 36 in. For the second pyramid, the height is 10 in. Plugging this height into the formula and using the previously calculated perimeter of 36 in, you get: Surface Area = 0.5 × 36 × 10 = 180 in. Therefore, the correct answer is B. 180 in.
7. The volume of a rectangular prism is given by: Volume = length × width × height. In this case, the width is given as 92 ft and the volume is 240 ft^3. Let's assume the length and the height of the similar prism are the same ratio as the width. So, the ratio of the widths is 46: 92, and we want to find the volume of the similar prism with a width of 46 ft. Let's call the volume of the similar prism V. Using the ratios, you have: (46/92) = (V/240). Cross-multiplying, you get 92V = 46(240), which simplifies to 92V = 11040. Dividing both sides by 92, you get V = 11040/92 = 120 ft^3. Therefore, the correct answer is D. 120 ft.