3.A rectangular prism has a width of 92ft and a volume of 240ft.Find the volume of a similar prism with a width of 23ft.Round to the nearest tenth, if necessary.
4.A pyramid a height of 5in. and a surface area of 90in^2.Find the surface area of a similar pyramid with a height of 10in. Round to the nearest tenth if necessary.
For numbers5-7 find the indicated measurement of the figure described.use 3.14 for pie and round to the nearest whole number
5.Find the surface area of a sphere with a radius of 8 cm.
6.Find the surface ares of a sphere with a radius of 12m.
7.Find the volume of a sphere with the a radius of 4ft.
I NEED HELP PLEASE ASAP
B
A
C
D
A
A
A
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bruh i got 2/7
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2 cm
12 mm
3.8 ft^3
360 in.^2
804 cm^2
1809 m^2
268 ft^3
3. To find the volume of a rectangular prism, you multiply the length, width, and height together. Given that the width of the first prism is 92ft and its volume is 240ft, we can use the formula:
Volume = Length x Width x Height
240 = Length x 92 x Height
We don't have enough information to find the lengths, so we cannot directly find the volume of the second prism. However, since the two prisms are similar, we can use the concept of similar figures.
Similar figures have proportional sides. Therefore, the ratio of the corresponding sides of both prisms will be the same. In this case, the ratio of the widths is:
92 / 23 = 4
So, the width of the second prism is 1/4 of the width of the first prism. Since volume is proportional to the side lengths cubed, we can conclude that the volume of the second prism is:
Volume of second prism = (1/4)^3 x 240
Volume of second prism ≈ 15ft^3
4. To find the surface area of a pyramid, you need to know the area of the base and the area of each triangular face. We know that the surface area of the first pyramid is 90in^2. However, without the height or any other dimensions, we cannot find the exact surface area of the second pyramid.
Similar to the previous question, the two pyramids are similar figures. This means their corresponding sides are proportional. Since only the height is provided, we can use a similar method to find the ratio:
Height of second pyramid / Height of first pyramid = 10 / 5 = 2
This means the height ratio is 2. Since the ratio of heights is squared, we can conclude that the surface area of the second pyramid is:
Surface area of second pyramid ≈ (2)^2 x 90 in^2
Surface area of second pyramid ≈ 360 in^2
5. The surface area of a sphere can be found using the formula:
Surface Area = 4πr^2
Given that the radius of the sphere is 8 cm, we can substitute this value into the formula:
Surface Area = 4 x 3.14 x (8 cm)^2
Surface Area ≈ 803 cm^2
6. Similarly, for a sphere with a radius of 12 m, we can use the same formula:
Surface Area = 4πr^2
Substituting the radius:
Surface Area = 4 x 3.14 x (12 m)^2
Surface Area ≈ 1809 m^2
7. Finally, to find the volume of a sphere, we use the formula:
Volume = (4/3)πr^3
Given that the radius of the sphere is 4 ft, we can substitute this value into the formula:
Volume = (4/3) x 3.14 x (4 ft)^3
Volume ≈ 268 ft^3
Remember to round your answers to the nearest tenth or whole number as specified in the problem.
3. 60ft
4. 180in
connnections academy
1.D
2.A
3.A
4.A
5.B
6.A
7.C