<p>Does anyone know how to solve Question 24 in Section 4 (p. 99) of the Upper Level Test 1 in the SSAT Official Guide Book. It is about the diameter of a soup can that serves 1/4 volume of the original serving but in the same height can -- Grandma's Soup Company. The answer key says it is 2 square root 2 (E) but my D's math teacher says it is (D) 4. If you know the steps to reach the answer in the book, please post here!! Help.</p>
<p>Grandma's Soup Company packages tomato soup that serves four i cylindrical cans having a base diameter 8 cm and a height of 10cm. It wants to introduce the soup in single-serving cans as well. If the company keeps the height of the new can at 10 cam, what should its new base diameter equal?</p>
<p>A. 1
B. The square root of 2
C. 2
D. 4
E. 2 time the square root of 2</p>
<p>You can eliminate both H and pi from the equation as those are constants, and look for the radius of a circle that is 1/4 the area of the original. The square of the new radius should be 1/4 the square of the original. Thus, the square of the new radius should be 1/4 of 16. Find the square root of 4, double it, and get 4: answer D. Check your work by plugging the numbers into the equation V = Pi * radius squared * H. Although there are more elegant ways of doing it, here is an off the cuff step by step:
Radius of original can=4
Radius of new (smaller) can=x
1/4 V = NewV
1/4 pi<em>4</em>4<em>10=pi</em>x<em>x</em>10
1/4<em>4</em>4=x<em>x
4=x</em>x
2=x
New diameter = 2x
New diameter = 4</p>
<p>More generally, if you just remember that a circle’s area will always follow the inverse square law of the radius, you know that to quarter the area you simply need to halve the radius no matter what the actual measurement. So halving the diameter would work as well when looking for volume. So if you know this law you can skip the formula and just simplify the question to what it is actually asking. If they are looking for a cylinder with a quarter of the volume but the same height, just look at what the diameter is and halve it. The can could have been 8.2446 cm. You would not need to do any actually figuring to know the new diameter would be 4.1223. This is probably why the question was written to find a can with 1/4 the original volume. Kids who know this shortcut can simply do it in 5 seconds and move on to he next question, saving their time for calculations they need more time for.</p>
<p>Thanks for your reply, Blairparent. That is what I did and the math teacher as well. But the answer key said the answer is E. I wrote to the ssat.org and they checked it out and determined the answer key was in error, so problem solved.</p>
<p>Here is the reply I received.</p>
<p>"Good morning,</p>
<p>Thank you for reaching out and sharing your query with us. We highly value and appreciate your feedback! After researching question #24 on page 99 in Math Section 4, I concluded that the correct answer is (D) 4. Because the answer key is incorrect, I’ve asked our marketing team to post the correct answer on our website.</p>
<p>Thank you again for sharing your discovery with us.</p>
<p>Best regards,
Kristy</p>
<p>Kristy L. Leirer
SSATB l Senior Examination Editor
t: 609.436.6139
<a href=“http://www.admission.org”>www.admission.org</a> I <a href=“http://www.ssat.org”>www.ssat.org</a>"</p>