A rectangular prism has a width of 92 ft and a volume of 240 ft^3. Find the volume of a similar prism with a width of 23 ft.
Round to the nearest tenth, if necessary.
•3.8 ft^3
•60 ft^3 <<<<<<
•15 ft^3
•10.4 ft^3
A pyramid has a height of 5 in. and a surface area of 90 in^2. Find the surface area of a similar pyramid with a height of 10 in.
Round to the nearest tenth, if necessary.
•360 in. ^2
•180 in. ^2 <<<<<<
•22.5 in. ^2
•3.6 in. ^ 2
If it is similar, then ALL the dimensions, not just the height, are doubled.
If you double lengths, you quadruple areas
A = k L^2
90 * 4 = 360 in^2
So... is the 1st one is correct?
A rectangular prism has a width of 92 ft and a volume of 240 ft^3. Find the volume of a similar prism with a width of 23 ft.
Round to the nearest tenth, if necessary.
•3.8 ft^3
•60 ft^3 <<<<<<
•15 ft^3
•10.4 ft^3
23/92 = .25
.25^3 = .015625
.015625 * 240 = 3.75 ft^3
I did not read it carefully.
To find the volume of a similar rectangular prism, you need to determine the scale factor between the original prism and the similar prism. The scale factor is the ratio of the corresponding side lengths of the two prisms.
In this case, the width of the original prism is 92 ft, and the width of the similar prism is 23 ft. The scale factor can be found by dividing the width of the similar prism (23 ft) by the width of the original prism (92 ft):
Scale factor = width of similar prism / width of original prism = 23 ft / 92 ft
Simplifying the ratio, we have:
Scale factor = 1/4
Since volume is a cubic measurement, the scale factor cubed is used to find the volume of the similar prism.
Therefore, the volume of the similar prism can be found by multiplying the scale factor by the volume of the original prism:
Volume of similar prism = (Scale factor)^3 * Volume of original prism
= (1/4)^3 * 240 ft^3
Calculating, we have:
Volume of similar prism = (1/64) * 240 ft^3
= 3.75 ft^3 (rounded to the nearest tenth)
So the correct answer is 3.8 ft^3.
Similarly, to find the surface area of a similar pyramid, you need to determine the scale factor between the original pyramid and the similar pyramid. The scale factor is the ratio of the corresponding heights of the two pyramids.
In this case, the height of the original pyramid is 5 in, and the height of the similar pyramid is 10 in. The scale factor can be found by dividing the height of the similar pyramid (10 in) by the height of the original pyramid (5 in):
Scale factor = height of similar pyramid / height of original pyramid = 10 in / 5 in
Simplifying the ratio, we have:
Scale factor = 2
Since surface area is a squared measurement, the scale factor squared is used to find the surface area of the similar pyramid.
Therefore, the surface area of the similar pyramid can be found by multiplying the scale factor squared by the surface area of the original pyramid:
Surface area of similar pyramid = (Scale factor)^2 * Surface area of original pyramid
= (2)^2 * 90 in^2
Calculating, we have:
Surface area of similar pyramid = 4 * 90 in^2
= 360 in^2 (rounded to the nearest tenth)
So the correct answer is 360 in^2.