Home
Class 12
MATHS
The glass pictured above can hold a maxi...


The glass pictured above can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces.
What is the value of k, in centimeters?

A

2.52

B

7.67

C

7.79

D

10.11

Text Solution

Verified by Experts

The correct Answer is:
D
Using the volume formula `V = (7pik^3)3/48` and the given information that the volume of the glass is 473 cubic centimeters, the value of k can be found as follows:
`473=(7pik^3)/48`
`k^3 =(473(48))/(7pi)`
`k=root3((473(48))/(7pi))~~10.10690`
Therefore, the value of k is approximately 10.11 centimeters.
Choices A, B, and C are incorrect. Substituting the values of k from these choices in the formula results in volumes of approximately 7 cubic centimeters, 207 cubic centimeters, and 217 cubic centimeters, respectively, all of which contradict the given information that the volume of the glass is 473 cubic centimeters.
Promotional Banner

Similar Questions

Explore conceptually related problems

The glass pictured above can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces. Water pours into the glass slowly and at a constant rate. Which of the following graphs best illustrates the height of the water level in the glass as it fills?

The maximum volume of the Erlenmeyer flask pictured above is 3.49 cubic inches, which is approximately 5.7 liters. What is the value of c, in inches?

An oil tank has the shape of a right circular cylinder is 12 centimeters in height and has a volume of 108 pi cubic centimeters. What is the diameter of the base of the cylinder, in centimeters?

What is the volume, in cubic centimeters,of the height circular cone in the figure above, in term of pi ?

In the figure above of a right circular cone, what is the approximate number of cubic centimeters in the volume of cone?

A troy ounce is a unit of mass used for precious metals such as gold. There are 12 troy ounces in a troy pound and a troy pound is equivalent to 373.3 grams. If the density of gold is 19.3 grams per cubic centimeter, which of the following is closest to the number of cubic centimeters in the volume of block of gold with mass of 5 troy ounces? [ Note: density is mass divided by volume]

A jeweler makes beads for a bracelet by melting silver into spherical molds. Each mold has a diameter of 1 centimeters. After the silverhardents, the jeweler drills a small cylindrical hole through the center of the bead for the chain as shown. The drill bit has a diameter of 4 millimeters. If the jeweler strings a total of 15 beads on an elastic band, what is the approximate volume of silver, in cubic centimeters, on the bracelet? (Note: There are 10 millimeters in 1 centimeter.) Note: The volume is approximate because the top and bottom of the cylindrical piece that is drilled out is slightly curved.

A square piece of cardbroad measuring x inches by x inches is to be used to form an open box by cutting off 2-inch squares, and then folding the slides up along the dotted lines, as shown in the figure above. If x is an integer , and the volume of the box must be greater than 128 cubic inches , what is the smallest value of x that can be used ?

Jenny has a pitcher that contains 1 gallon of water. How many times could Jenny completely fill the glass with approximately 16 fluid ounces? (1 gallon = 128 fluid ounces)

The slant height of a pyramid is the perpendicular distance from the vertex of the pyramid to the base of a figure above, the height is labeled h, the length of a side of the square base is 24 cm, and the slant height is 15 cm, What is the volume , in cubic centimeters, of the pyramid?