Find the surface area and volume of a sphere with radius 9 yards.
Use 3.14 for π.
RESPOND TO EACH STATEMENT
BE SURE TO LABEL YOUR RESPONSES WITH THE APPROPRIATE LETTER
A) What formula will you use for the surface area of the sphere
B) What is the surface area
C) What formula will you use for the volume of the sphere
D) What is the volume of the sphere
A) The formula for the surface area of a sphere is 4πr^2
B) The surface area of the sphere with a radius of 9 yards is 1017.36 square yards.
C) The formula for the volume of a sphere is (4/3)πr^3
D) The volume of the sphere with a radius of 9 yards is 3053.63 cubic yards.
Solve the problem.
A cubical container measures 3 m on each edge.
What does it cost to fill the container at $2.47 per cubic m?
RESPOND TO EACH STATEMENT
BE SURE TO LABEL YOUR RESPONSES WITH THE APPROPRIATE LETTER
A) What is the volume of the container
B) What is the volume in cubic meters
C) What will it cost to fill the container
D) If there is 7.5% sales tax on the material to fill the container, what will you pay to fill the container
A) The volume of the container is determined by multiplying the length of each edge: 3m * 3m * 3m = 27 cubic meters.
B) The volume of the container is 27 cubic meters.
C) To find the cost to fill the container, multiply the volume (27 cubic meters) by the cost per cubic meter ($2.47): 27 cubic meters * $2.47 per cubic meter = $66.69
D) If there is a 7.5% sales tax on the material to fill the container, you will need to add 7.5% of the cost to fill the container to the total cost. 7.5% of $66.69 = $5.00. Therefore, the total cost to fill the container including sales tax is $66.69 + $5.00 = $71.69.
Solve the problem.
A church steeple casts a shadow 114 ft long, and at the same time a 8.0-ft post casts a shadow 5.0 ft long.
How high is the steeple?
Round to the nearest unit.
RESPOND TO EACH STATEMENT
BE SURE TO LABEL YOUR RESPONSES WITH THE APPROPRIATE LETTER
A) What is equation will you use to solve the problem
B) What is the height of the steeple
C) What is the angle of elevation from the end of the shadow to the top of the post
D) What is the length of a wire attached to the top of the steeple and anchored at the end of the shadow
A) We will use the concept of similar triangles to solve the problem.
B) To find the height of the steeple, we will set up a proportion between the lengths of the shadows and the heights of the steeple and the post: (height of steeple) / (shadow of steeple) = (height of post) / (shadow of post). Plugging in the values given, (height of steeple) / 114 = 8.0 / 5.0. To solve for the height of the steeple, we can cross multiply and divide: (height of steeple) = (8.0 / 5.0) * 114.
C) To find the angle of elevation from the end of the shadow to the top of the post, we can use the inverse tangent function. Using the height of the post (8.0 ft) and the shadow of the post (5.0 ft), the angle of elevation is equivalent to the inverse tangent of (height of post / shadow of post). Using a calculator, we can find the angle of elevation.
D) To find the length of the wire attached to the top of the steeple and anchored at the end of the shadow, we can use the Pythagorean theorem. The length of the wire is the hypotenuse of a right triangle, with the height of the steeple as one side and the shadow of the steeple as the other side.
A) The formula for the surface area of a sphere is A = 4πr^2, where r is the radius of the sphere.
B) To find the surface area, we substitute the given radius (r = 9 yards) into the formula:
A = 4π(9)^2 = 4π(81) = 324π square yards.
C) The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.
D) To find the volume, we substitute the given radius (r = 9 yards) into the formula:
V = (4/3)π(9)^3 = (4/3)π(729) = 972π cubic yards.
A) The formula for the surface area of a sphere is A = 4πr^2, where A represents the surface area and r represents the radius.
B) To find the surface area, substitute the given radius of 9 yards into the formula. Using π ≈ 3.14, the calculation will be A = 4 * 3.14 * 9^2.
C) The formula for the volume of a sphere is V = (4/3)πr^3, where V represents the volume and r represents the radius.
D) To find the volume, substitute the given radius into the formula. Using π ≈ 3.14, the calculation will be V = (4/3) * 3.14 * 9^3.