Math 058 Sample Test 5
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3 ft
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The Circus Q horse ranch has a circular paddock with radius 30 feet. How many feet
of fencing will they need is they want to enclose it? Leave your answer in the form
n, where n is a number
r = 30, circumference = 2 π r, need 60 π feet of fence.
If the base of a triangle is 4 and its height is twice its base, what is its area?
A = ½ bh, b = 4, h = 2b = 8, A = (1/2)(4)(8) = 16
Find the area of the shaded region:
4 ft
2 ft
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10 ft
12 ft
8 ft
Break into rectangles: 4 x 12+ 8 x 9 + 2 x 10 = 48 + 72 + 20 = 140 square ft
A paint can is 10 inches tall and has circumference 6 inches. How much paint does
the can hold in terms of cubic inches?
V = π r2 h, 2π r = circumference = 6 π, so r = 6 π /(2π) = 3. V = π r2 h = π (9)10 =
90 π cubic inches
Bound the square root of 940 by integers. e.g., 3 < √15 < 4. Which of the integers you
found is a closer estimate of the square root?
900 = 30 x 30, 31 x 31 = 961, 30 < √940 < 31, closer to 31
The two legs (the two shortest sides) of a right triangle are 6 and 8 inches. What is
the length of the third side?
We know that 62 + 82 = x2. So 36 + 64 = 100 = x2, x = 10 inches
A cone has volume 18  cubic meters. If its radius is 3 meters, what is its height?
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V = 3 r2h = 18 π = πr2h/3 so 18 = r2h/3 = 9h/3 or h = 6 m
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Joe is building a rectangular box. If it is 3 inches by 6 inches by 10 inches, and a can
of paint covers 100 square inches, how much paint will he need to paint the outside
of the box?
The box has two sides 3 x 6 = 18, or 36 sq in, two sides 6 x 10, or 120 in, and two sides
3 x 10m or 60 in. The total area is 120 + 60 + 36 = 216 square incles. If one can does 100
square inches, he will need more than two cans, 2.16 cans. He should buy 3 cans.
The tallest building in Green Town is 350 feet tall. At 4 PM, it has a shadow whose
length is 70 feet. If Joe is 6 feet tall, how long is his shadow?
These are similar triangles 70/350 = x/6. 70/350 = 1/5 = x/6, x = 6/5 feet
A balloon, when it is full, holds 36 cubic inches of air. What is the balloon’s
diameter?
4𝜋𝑟 3
A balloon is a sphere. V =
= 36 π. 4r3/3 = 36, r3 = 36 (3/4) = 27
3
r3 = 27, r = 3 inches. So, the diameter is 6 inches.
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The area of a triangle is 32 inches. If its base is 4 inches, what is its height?
A = ½ bh = 32 = ½ (4) (h)
32 = 2h, h = 16 inches
The perimeter of a rectangular pasture is 240 feet. Its length is twice its width. What
is the area of the pasture?
P = 2L + 2W = 240. L = 2W, so P = 2(2W) + 2W = 6W = 240. W = 40 ft, L = 80 ft
Area = L x W = 40 x 80 = 3200 square feet
A pie is 10 inches in diameter and 1 inch deep. Each cubic inch of filling weighs 2 oz.
If the pie is cut into 10 pieces, what is the weight of each piece? Leave your answer in
terms of , for example, n  oz.
The pie is a cylinder. Its volume is π r2 h. r = ½ diameter = 5 in, h = 1.
V = 25(1) π cubic inches. If each cubic inch is 2 oz, we have 50 π oz, total. It is cut into
10 pieces; each is π 50/10 oz = 5 π oz
Joe has two triangles, A and B. In each of them, the smallest angle is half the largest
and the middle angle is ten degrees larger than the smallest. The largest side of
triangle A is 10 inches, and the smallest side is 5 inches. The largest side of triangle B
is 30 inches. What is the smallest side of triangle B?
The key is that the angles are the same for each triangle, thus they are similar
triangles. The largest side of A / largest side of B = smallest side of A / smallest side
of B. 10/5 = 30/x, or x/30 = 5/10. x = 150/10 = 15 inches
A right triangle has a perimeter 12 feet. The shortest side is 2 inches shorter than the
longest, and the middle side is 1 inch shorter than the longest. What is the area of the
triangle?
sides are A, B, C, in order of size. C = A-2, B = A-1.
Perimeter = A + B + C = A + A-1 + A-2 = 3A – 3 = 12. 3A = 9, A = 3. Sides are 3, 4, 5.
Now, this is a right triangle, which means that its height is one leg and its base is the
other. A = ½ bh.
Therefore, its area is 3x4/2 = 6 square feet