Use the image to answer the question.
An oblique cone shows a base radius of 9 inches. The perpendicular height is 5 inches from the apex to the base outside the cone. A right angle is formed outside the cone to the right. A dashed diagonal line connects the center of the circular base to the apex.
What is the volume of the cone? Use 3.14 for pi.
(1 point)
Responses
942 cubic inches
942 cubic inches
423.9 cubic inches
423.9 cubic inches
235.5 cubic inches
235.5 cubic inches
47.1 cubic inches
47.1 cubic inches
Vol = (1/3) * π * r^2 * h
r = 9 inches, h = 5 inches
Vol = (1/3) * 3.14 * 9^2 * 5
Vol = (1/3) * 3.14 *81 * 5
Vol = (1/3) * 3.14 * 405
Vol = 423.9 cubic inches
Therefore, the volume of the cone is 423.9 cubic inches.
A professional baker uses a chocolate mold to make decorations for cakes. One chocolate mold is in the shape of a cone and has a diameter of 2 cm and a height of 6 cm. What volume of chocolate, in cubic centimeters, is needed to make a solid chocolate cone? Use 3.14 for π
.(1 point)
Responses
12.56 cubic centimeters
12.56 cubic centimeters
6.28 cubic centimeters
6.28 cubic centimeters
18.84 cubic centimeters
18.84 cubic centimeters
37.68 cubic centimeters
First we need to find the radius of the base of the cone:
radius = diameter/2 = 2 cm / 2 = 1 cm
Now we can use the formula for the volume of a cone:
V = (1/3)*π*r^2*h
V = (1/3)*3.14*(1^2)*6
V = (1/3)*3.14*1*6
V = (1/3)*18.84
V = 6.28 cubic centimeters
Therefore, the volume of chocolate needed to make the solid chocolate cone is 6.28 cubic centimeters.
Find the surface area of a sphere with a radius of 3.6 ft. Use 3.14 for pi. Round your answer to the nearest hundredth, if necessary.(1 point)
The formula for the surface area of a sphere is:
SA = 4πr^2
Given that the radius, r, is 3.6 ft, we can substitute this into the formula:
SA = 4 * 3.14 * (3.6)^2
SA = 4 * 3.14 * 12.96
SA = 51.84 * 3.14
SA = 162.8176
Rounded to the nearest hundredth, the surface area of a sphere with a radius of 3.6 ft is 162.82 square feet.