A post tree outside of matts house casts a 12 foot shadow at a certain time of day. At the same time matt, who is 6 feet tall, casts a 2 foot shadow. How tall is the tree?
How do I solve this?
The marketing department of the company is considering making a keychain with a miniature replica of their top selling dishwasher detergent. The dimensions of the dishwasher detergent box are 9 inches by 7.5 inches by 2.25 inches. If the replica will be 1/5 the size of the regular box, what will be the volume of the miniature box?
How do I solve this?
Proportion
6 /2ft=H/12
solve for H.
Volume box=8*7.5*2.25 * (1/5^3) inches cubed.
To solve the first question, we can use a proportion to determine the height of the tree.
Let's set up the proportion:
Height of the tree / Length of the tree's shadow = Height of Matt / Length of Matt's shadow
We know that the height of Matt is 6 feet and his shadow is 2 feet. The length of the tree's shadow is given as 12 feet.
Substituting the values:
Height of the tree / 12 = 6 / 2
Simplifying the equation:
Height of the tree / 12 = 3
Now cross-multiply:
Height of the tree = 12 * 3
Height of the tree = 36 feet
Therefore, the tree is 36 feet tall.
To solve the second question about the volume of the miniature box, we can use the concept of scale factors.
The original dimensions of the dishwasher detergent box are given: 9 inches by 7.5 inches by 2.25 inches.
If the replica will be 1/5 the size of the regular box, it means each dimension of the replica will be 1/5 of the original dimension.
To find the dimensions of the miniature box, multiply each dimension of the original box by 1/5:
Length of the miniature box = 9 inches * 1/5 = 1.8 inches
Width of the miniature box = 7.5 inches * 1/5 = 1.5 inches
Height of the miniature box = 2.25 inches * 1/5 = 0.45 inches
Now, calculate the volume of the miniature box by multiplying the dimensions:
Volume of the miniature box = Length * Width * Height = 1.8 inches * 1.5 inches * 0.45 inches
Simplifying the expression:
Volume of the miniature box = 0.6075 cubic inches
Therefore, the volume of the miniature box will be approximately 0.6075 cubic inches.