A cylindrical vase has a diameter of 6 inches. At the bottom of the vase, there are 9 marbles, each of diameter 3 inches. The vase is filled with water up to a height of 12 inches. Which of the following could be used to calculate the volume of water in the vase?

π(3in)2(12in) − 1.5(four over threeπ(9in)3)
π(12in)2(3in) − 1.5(four over threeπ(9in)3)
π(3in)2(12in) − 9(four over threeπ(1.5in)3)
π(12in)2(3in) − 9(four over threeπ(1.5in)3)

4

Step-by-step explanation:

To find:

The remainder, when 3^0 + 3^1 + 3^2 + ... +3^2009 is divided by 8

Approach and Working:

Rem (3^0/8) = 1

Rem (3^1/8) = 3

Rem (3^2/8) = 1

Rem (3^3/8) = 3

Rem (3^4/8) = 1

Rem (3^5/8) = 3 and so on…

We can observe that,

For even powers of 3, the remainder is 1

And for odd powers of 3, the remainder is 3.

Therefore, we can rewrite the given series, in terms of its remainders, as

= 1 + 3 + 1 + 3 + 1 + 3 + … + 3 = 1005 pairs of (1 + 3) = 1005 x 4 = 4020

Rem (4020/8) = 4