the body e example of this is prostate cancer The prostate is a gland that often becomes cancerous in men as they age Cancerous prostate cells secrete a prostate specific antigen or PSA A blood te PSA is recommended for men over the age of 50 and is often used as a first warning of possible cancer e way of dealing with prostate cancer is to surgically remove the gland prostatectomy After that has been done there should be no cancer cells left and therefor no PSA found in the blood ce it s hard to get all the cancer cells and some may escape after a prostatectomy regular tests for PSA are done to detect possible presence and growth of cancer cells Another way to loo such metastatic cancer is with an MRI Magnetic Resonance Imaging or CT Computerized Tomography scan In this problem we ll estimate which method is more sensitive spherical tumor 3 cm in diameter consisting of prostate cells may result in a PSA blood level of about 20 nanograms milliliter of blood The most common test can only detect the presence of A in the blood if it is greater than about 0 1 ng ml An MRI can detect a cancerous tumor down to about a diameter of 1 mm hich is a more sensitive test for the return of prostate cancer the blood test or an MRI 33 Part a To decide this estimate the diameter in mm of a tumor that would produce a PSA level just less than 0 1 ng ml d sin cotan mm cos asin tan T acos E 4 sinh k 1 7 8 5 2 9 6 3 HOME Grade Summary Deductions Potential 0 100 Submissions Attempts remaining 6 2 per attempt