1. A rectangular prism has a width of 92 ft and a volume of 240 ft3. Find the volume of a similar prism with a width of 23 ft. Round to the nearest tenth, if necessary.
a)3.8 ft3
b)60 ft3
c)15 ft3
d)10.4 ft3
2.A pyramid has a height of 5 in. and a surface area of 90 in2. Find the surface area of a similar pyramid with a height of 10 in. Round to the nearest tenth, if necessary.
a)360 in2
b)180 in2
c)22.5 in2
d)3.6 in2
1. b
2. a
1 is 3.8 kelsey
1. To find the volume of a similar prism, we can use the concept of proportional reasoning. Since the width of the two prisms are in a ratio of 92:23, we can assume that the height and length are also in the same ratio. Let's call the height and length of the first prism "h1" and "l1", respectively, and the height and length of the second prism "h2" and "l2", respectively.
According to the given information:
Width of the first prism (w1) = 92 ft
Volume of the first prism (V1) = 240 ft^3
We can set up the following proportion:
(w1/w2)^3 = (V1/V2)
Substituting the given values into the proportion:
(92/23)^3 = (240/V2)
Simplifying the equation:
(4)^3 = 240/V2
64 = 240/V2
Now, we can solve for V2 (the volume of the second prism):
V2 = (240/64)
V2 = 3.75 ft^3
Rounding to the nearest tenth, the volume of the similar prism with a width of 23 ft is approximately 3.8 ft^3.
Therefore, the correct answer is option a) 3.8 ft^3.
2. To find the surface area of a similar pyramid, we can also use the concept of proportional reasoning. Since the height of the two pyramids are in a ratio of 5:10, we can assume that the base area is also in the same ratio. Let's call the base area of the first pyramid "A1" and the base area of the second pyramid "A2".
According to the given information:
Height of the first pyramid (h1) = 5 in
Surface area of the first pyramid (SA1) = 90 in^2
We can set up the following proportion:
(h1/h2)^2 = (SA1/SA2)
Substituting the given values into the proportion:
(5/10)^2 = (90/SA2)
Simplifying the equation:
(1/2)^2 = (90/SA2)
1/4 = (90/SA2)
Now, we can solve for SA2 (the surface area of the second pyramid):
SA2 = (90/1/4)
SA2 = 360 in^2
Rounding to the nearest tenth, the surface area of the similar pyramid with a height of 10 in is approximately 360 in^2.
Therefore, the correct answer is option a) 360 in^2.