Question

question 6: standard g.gmd.3
spheres only need ___ to be able to find their volume.
a. radius
b. height
c. base area
d. pi
question 7: standard g.gmd.3
pyramids and cones only take up ___ the space of a regular 3d shape.
a. ½
b. ⅓
c. ¼
d. ⅕
question 8: standard g.gmd.3
if the radius of a sphere is 4 cm, what is its volume?
a. 148
b. 42
c. 268
d. 340
question 9: standard g.gmd.3
a square based pyramid has an area of 4 cm². the height of the pyramid is 7 cm. what is the volume?
a. 28
b. 9.3
c. 3.2
d. 112
question 10: standard g.gmd.3
a hexagonal prism has a base with an area of 50 in² and a height of 4 in. what is the volume?
a. 200
b. 100
c. 75
d. 50

Explanation:

Question 6

The formula for the volume of a sphere is \( V = \frac{4}{3}\pi r^3 \), where \( r \) is the radius. Height is not a dimension of a sphere, base area is for other shapes, and pi is a constant, not a measurement needed to find the volume (since it's a known constant). So only the radius is needed.

The volume of a pyramid or cone is \( \frac{1}{3} \) the volume of a prism or cylinder (regular 3D shapes with the same base and height). So they take up \( \frac{1}{3} \) the space.

Step1: Recall the volume formula for a sphere.

The formula for the volume of a sphere is \( V=\frac{4}{3}\pi r^{3} \).

Step2: Substitute the radius \( r = 4 \) cm into the formula.

\( V=\frac{4}{3}\pi(4)^{3}=\frac{4}{3}\pi\times64=\frac{256}{3}\pi\approx\frac{256}{3}\times3.14\approx267.95\approx268 \) \( \text{cm}^3 \).

Answer:

a. Radius

Question 7