Four similar glass tumblers just fit into a cubical box.The area of the top of the circular cover of any one of the tumblers is 4 pi.The area of each side of the box is
a. 16
b. 32
c. 32 pi
d. 64
e. 64 pi
please answer and explain
do this. Get 4 quarters, put the first one on the corner of a piece of paper. Now add the other three.
I think the smallest square you can get with the quarters enclosed is will have twice the diameter of any quarter.
areaaqarter= (D/2)^2 PI= 4PI
Diameter= 4 inches. area box side= 2*diatmeter.
I still not get it
To find the area of each side of the box, we need to determine the dimensions of the box.
Let's consider one tumbler. The circular cover of the tumbler has an area of 4π. The area of a circle is given by the formula A = πr^2, where r is the radius. Since the area of the top of the tumbler is 4π, we can solve for the radius:
4π = πr^2
Dividing both sides by π:
4 = r^2
Taking the square root of both sides:
2 = r
So, the radius of the circular cover of the tumbler is 2.
A cubical box can perfectly accommodate four tumblers. Since the tumblers fit perfectly, each side of the box should be equal to the height of one tumbler plus two times the radius of the circular cover.
The height of the tumbler can be determined by calculating the diameter of the circular cover and subtracting two times the radius:
Diameter = 2 × radius = 2 × 2 = 4
Height = Diameter - 2 × Radius = 4 - 2 × 2 = 4 - 4 = 0
Therefore, the height of one tumbler is 0.
The dimensions of the box are height = 0, width = diameter of the circular cover = 4, and length = diameter of the circular cover = 4.
To find the area of each side of the box, we need to calculate the area of a rectangle given its dimensions.
Area of a rectangle = length × width
Area of each side of the box = 4 × 4 = 16
So, the answer is (a) 16, and each side of the box has an area of 16.
Therefore, the correct answer is (a) 16.