Which one of these statements is true about summaries?
A summary is a condensed version of a text that captures the main points and key ideas.
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The volume of a tree stump can be modeled by considering it as a right cylinder. Lillian measures its height as 1.1 ft and its radius as 22 in. Find the volume of the stump in cubic inches. Round your answer to the nearest tenth if necessary.
First, we need to convert the height and radius to the same units. Let's convert the radius to feet:
22 in = 22/12 ft = 1.8333 ft (rounded to four decimal places)
Now we can use the formula for the volume of a right circular cylinder:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
Plugging in the values we have:
V = π(1.8333)^2(1.1)
V ≈ 11.845 cubic feet
To convert cubic feet to cubic inches, we need to multiply by (12 inches/1 foot)^3 to get:
V = 11.845 x (12)^3 cubic inches
V ≈ 2,561.4 cubic inches (rounded to the nearest tenth)
Therefore, the volume of the tree stump in cubic inches is approximately 2,561.4 cubic inches.
The volume of a tree stump can be modeled by considering it as a right cylinder. Makayla measures its height as 1.3 ft and its radius as 6 in. Find the volume of the stump in cubic inches. Round your answer to the nearest tenth if necessary.
First, let's convert the radius to feet:
6 in = 6/12 ft = 0.5 ft
Now we can use the formula for the volume of a right circular cylinder:
V = πr^2h
where V is the volume, r is the radius, and h is the height.
Plugging in the values we have:
V = π(0.5)^2(1.3)
V ≈ 0.845 cubic feet
To convert cubic feet to cubic inches, we need to multiply by (12 inches/1 foot)^3 to get:
V = 0.845 x (12)^3 cubic inches
V ≈ 1,454.1 cubic inches (rounded to the nearest tenth)
Therefore, the volume of the tree stump in cubic inches is approximately 1,454.1 cubic inches.
The diameter of a circle is 13 in. Find the circumference
to
the
nearest
tenth
to the nearest tenth.
The circumference of a circle is found by multiplying the diameter by π (pi), which is approximately 3.14159.
So, if the diameter of the circle is 13 inches, then the circumference is:
C = πd
C = 3.14159 x 13
C ≈ 40.8407
Rounding this to one decimal place gives:
C ≈ 40.8
Therefore, the circumference of the circle, to the nearest tenth, is approximately 40.8 inches.
The circumference of a circle is 14
π m. Find its diameter, in meters.
We know that the circumference of a circle can be found using the formula:
C = πd
where C is the circumference and d is the diameter.
In this case, we are given that the circumference is 14π meters. So, we can set up the equation as:
14π = πd
To solve for d, we can divide both sides by π:
14π/π = d
Simplifying the left side gives:
14 = d
Therefore, the diameter of the circle is 14 meters.
The radius of a circle is 6 cm. Find its area to the nearest whole number.
The formula for the area of a circle is:
A = πr^2
where A is the area and r is the radius.
Given that the radius is 6 cm, we can plug this value into the formula and simplify:
A = π(6)^2
A = π(36)
A ≈ 113.1
Rounding this to the nearest whole number gives:
A ≈ 113
Therefore, the area of the circle, to the nearest whole number, is approximately 113 square centimeters.
Find the Area of the figure below, composed of a rectangle and a semicircle. The radius of the circle is shown. Round to the nearest tenths place.
We can start by finding the area of the rectangle and the area of the half-circle separately and then adding them together to get the total area.
The area of the rectangle is:
A_rect = L x W
where L is the length and W is the width. In this case, the rectangle has a length of 10 cm and a width of 6 cm, so we can plug these values into the formula:
A_rect = 10 cm x 6 cm = 60 square cm
The area of the half-circle is:
A_hc = (1/2) x π x r^2
where r is the radius of the circle. In this figure, the radius is 4 cm, so we can plug this value into the formula:
A_hc = (1/2) x π x (4 cm)^2
A_hc ≈ 25.13 square cm
To get the area of the entire figure, we add the area of the rectangle and the area of the half-circle:
A_total = A_rect + A_hc
A_total = 60 square cm + 25.13 square cm
A_total ≈ 85.13 square cm
Rounding to the nearest tenth gives:
A_total ≈ 85.1 square cm
Therefore, the area of the figure, rounded to the nearest tenth, is approximately 85.1 square centimeters.