Study Guide in Geometry

Find the volume.

• 80 cubic cm

• 108 cubic cm

• 28 cubic cm

• 145 cubic cm

While solving circle area problems, you are often given the measure of the diameter. Do NOT put the diameter into the area formula. Instead...

• Half the diameter to find the radius.

• Double the diameter to find the radius.

Answer explanation

The radius times two equals the diameter. Take a look at the picture. If you plug in the diameter instead of the radius, I can almost guarantee you'll find that wrong answer as an answer choice.

The diameter of a circular opening for a ceiling light is 4 inches. What is the approximate circumference of the opening?

Use 3.14 for pi.

• 6.3 inches

• 12.6 inches

• 25.1 inches

• 50.2 inches

Answer explanation

You are given that the diameter is 4 inches. Use that in the formula $C\ =\ \pi d$ .

A local pizza shop offers a large pizza with a diameter of 14 inches and an extra-large pizza with diameter of 16 inches. About how much larger is the area extra-large pizza compared to the area of a large?

• 2 square inches

• 15 square inches

• 47.1 square inches

• 188.5 square inches

Answer explanation

You need to find the area of each pizza (be careful to half the diameter to get the radius) and subtract to find the difference.

Large pizza: diameter of 14 inches

Extra-large pizza: diameter of 16 inches

What is the approximate area of the shaded region of this figure?

Use 3.14 for pi.

• 3 square units

• 6 square units

• 10 square units

• 13 square units

Answer explanation

The radius is 2 units, and the length of the square is 4 units. You need to find the area of the square and subtract the area of the circle to find the area of the shaded pieces.

What is the PERIMETER of the triangular base of this prism?

• 14 units

• 6 units

• 12 units

• 24 units

Answer explanation

The three (3) side lengths of the triangle face are 4, 3, and 5, for a total perimeter of 4+3+5=12.

What is the combined area of the rectangles of this prism?

Remember, it's the perimeter of the triangle face times the height of the prism.

• 19 units²

• 47 units²

• 84 units²

• 24 units²

Answer explanation

To find the combined area of the three (3) rectangular sides, you need to know that the peri7(meter of the triangle is the long side of the pink rectangle shown.

That makes the combined rectangle (bottom right) a 7(12)=84 square inch area.

Find the volume of the prism.

• 1080 cm³

• 450 cm³

• 540 cm³

• 360 cm³

Answer explanation

Again, just like in the surface area problem with the same triangular prism, you need to know that the base and height of a triangle might not always be the bottom length as the base and a straight up and down length as the height. Imagine turning this triangular prism 90 degrees to the left to see the 9 inches as the base and the 12 inches as the height of the triangle.

For finding volume, the 15 inches length is not needed.

Find the volume. Be careful to note that there is an extra measurement you need only when calculating surface area, not volume.

• 136.08 in³

• 115.2 in³

• 216.75 in³

• 43.56 in³

Answer explanation

The extra measurement is the slant height, or the height of the triangular faces. You will not need to use the 16 inch length to find the volume of this pyramid with the formula $V\ =\frac{1}{3}Bh$ .

Find the area of the trapezoid (composite figure).

• 54 ft²

• 82 ft²

• 88 ft²

• 91 ft²