# Tutor profile: Benjamin P.

## Questions

### Subject: SAT II Mathematics Level 1

A hollow sphere with a diameter of 10 inches contains a smaller, solid sphere with a radius of 1.5 inches. Calculate the amount of empty space within the larger sphere.

To solve this problem, we must first find the total volume of the larger sphere and subtract from it the volume of the smaller sphere. This will give us the total volume of empty space within the system. The formula for the volume of a sphere is V = (4/3) π r^3 If the diameter of the larger sphere is 10 inches, the radius must be 5 inches. The volume of the larger sphere when r = 5 must be V = (4/3) π (5)^3 = (4/3) π (125) = (500/3)π inches^3. The radius of the smaller sphere is 1.5 inches, which can be represented in fractional form as (3/2) inches. The volume of the smaller sphere when r = (3/2) inches must be V = (4/3) π (3/2)^3 = (4/3) π (27/8) = (108/24)π = (9/2)π inches^3. We now know that the total volume of the larger sphere is (500/3)π inches^3 and the total volume of the smaller sphere is (9/2)π inches^3. The final step is to subtract the volume of the smaller sphere from that of the larger sphere. Volume of Empty Space = (500/3)π - (9/2)π The common denominator is 6, so (500/3)π becomes (1000/6)π and (9/2)π becomes (27/6)π Volume of Empty Space = (1000/6)π - (27/6)π = (973/6)π inches^3 Therefore, the volume of empty space within the larger sphere is (973/6)π inches^3

### Subject: Biology

Describe how free ribosomes differ from bound ribosomes on the rough endoplasmic reticulum in a typical animal cell. Reference the final destinations of the protein and the pathway it takes to get there from each type of ribosome.

Free ribosomes float in the cytoplasm of a typical animal cell; their main purpose is to manufacture proteins to be used within the cell body. The mRNA arrives from the nucleus to such ribosomes and the protein is manufactured within the cytoplasm so it can be immediately released. In contrast, bound ribosomes on the rough endoplasmic reticulum (ER) manufacture proteins to be released into the extracellular matrix. Proteins made by bound ribosomes travel through the rough ER after completion and get sent to the Golgi Body, where they will get repackaged and sent to locations outside the cell.

### Subject: Anatomy

A healthy person will have reflexes that can be tested for by a physician, and such reflexes help to protect an individual from damaging objects or situations that may cause bodily harm. Using an example, describe the neural pathway of a typical reflex arc.

The patellar reflex is frequently checked when a physician is conducting an annual check-up. When the doctor strikes the patellar tendon in the knee, the sensory receptor sends an impulse through the afferent neuron to the spinal cord. In the spinal cord, an interneuron transmits this impulse to an efferent neuron that travels back through the body and to the muscles of the leg. The muscles act as the effectors of the reflex arc, snapping the leg towards a straightened position in an attempt to protect the exposed tendon.

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