In With The New solutions

Millions of people will fix their eyes on the ball dropping in Times Square this New Year’s Eve to indicate the end of 2019 and the beginning of 2020.  The famous ball is six feet in diameter and weighs 1070 pounds.  If the weight were distributed evenly throughout the ball, what would be the average number of pounds per cubic foot, to the nearest tenth?  (Assume that the ball is a perfect sphere, though its surface is actually made up of 504 small, crystal triangles.)

Snowman Geometry

For the following problems, assume that the snowballs are perfect spheres.

Chiquita and Rhonda are each building a snowman. Rhonda tells Chiquita that she is making each of her 3 balls of snow 20% smaller than the one below it. Rhonda starts by making the base ball with a diameter of 20 inches. If she reduces the diameter by 20% each time she makes a new ball, what is the diameter of the third ball she makes (the ball for the snowman’s head)? Express your answer as a decimal to the nearest tenth.

Best of 2018 School Competition

In honor of this year’s School Competition being released to registered competition coaches for our 2019-2020 Competition Series, see some of last year’s School Competition questions below!

Sprint Round, 19

Josie selected a number n. She divided n by 2 and then subtracted ½ from the result. She took half of that result and then subtracted ½ to get the final result of 10. What is the value of n?