Geometry Test

The diagram shows a triangular prism on top of a rectangular prism. Find the volume of this object.

• 87.5 cm³

• 387.5 cm³

• 300 cm³

• 1052.5 cm³

Answer explanation

Remember to always start with the shapes. Both the prisms are whole, so I will add the two volumes. Also see the two lines at the bottom have a congruent lines meaning they are the same length - 5 cm.

Volume = Volume of triangular prism + Volume of rectangular prism

V = (1/2)bh_th_p + lwh

V = (1/2)(7)(5)(5) + (5)(5)(12)

V = 87.5 + 300

V = 387.5 cm³

The diagram shows a cylindrical container of diameter 9 cm and height 14 cm filled with water. Mrs. Johnson pours the water into triangular moulds as shown to make Jello. (Take π = 22/7) How many of the triangular moulds are completely filled with water?

• 37

• 38

• 148

• 149

Answer explanation

Start by finding the volume in the water to start:

V = Area of base*Height of cylinder

V = πr²h

V = (22/7)(4.5)²(14)

V = 891 cm³

Now, find how much water 1 triangular mould can hold:

V = Area of base*Height of prism

V= (1/2)bh_th_p

V = (1/2)(4)(4)(3)

V = 24 cm³

Now you can divide the total volume by how much each triangular mould can hold.

891 ÷ 24 = 37.125

Therefore, you could fill 37 moulds completely.

The diagram shows a cylindrical container of diameter 9 cm and height 14 cm filled with water. Mrs. Johnson pours the water into triangular moulds as shown to make Jello. (Take π = 22/7)

Find the remainder of the water left in the cylindrical container.

• 3 cm³

• 12 cm³

• 21 cm³

• 24 cm³

Answer explanation

From the last problem, you know that there is 0.125 left over when you divide the volume of the cylinder by the volume of the triangular mould. This is the equivalent of 1/8.

So, I can multiply the full volume of the triangular mould by 1/8 to get the volume of the water left.

(1/8)(24) = 3 cm³ left

A circle has a radius of 7.6 cm. What is the diameter of the circle?

• 3.8 cm

• 7.4 cm

• 7.8 cm

• 15.2 cm

Answer explanation

Remember that a radius from the edge of the circle, while a diameter is from one point on the edge of the circle through the center of the circle to the opposite edge.

Also the formula: 2r = d

The diameter of a circle is 35 in. Find the circumference of the circle. (Take \(\pi=\frac{22}{7}\) )

• 55 in.

• 110 in.

• 165 in.

• 220 in.

Answer explanation

The formula for circumference of a circle is C = πd

The radius of a circle is 6 cm. Find its area. (Take π = 3.14)

• 18.84 cm²

• 28.26 cm²

• 37.68 cm²

• 113.04 cm²

Answer explanation

Formula for area of a circle:

A = πr²

A = (3.14)(6)²

A = 113.04 cm²

A circle has a circumference of 13.2 cm. Find the area of the circle.

• 3.465 cm^2

• 55.44 cm^2

• 13.86 cm^2

• 221.76 cm^2

Answer explanation

Start with the formula for circumference:
C = πd
13.2 = πd
Divide both sides by π.

$4.20\approx d$
So, we divide d in half to get r.
$2.10\approx r$
Now use the formula for area:
A = πr^2
A = (3.14)(2.10)^2
A = 13.86 cm^2

The figure shows two quarter circles within a rectangle.

(Take π = 22/7)

Find the perimeter of the shaded part.

• 36 in.

• 58 in.

• 64 in.

• 86 in.

Answer explanation

To find the perimeter of a composite figure, add all the parts up until you go all the way around the figure.

Perimeter = curved 1/4 of circle + curved 1/4 of circle + straight line

P = (1/4)πd + (1/4)πd + 14

P = (1/4)(22/7)(14) + (1/4)(22/7)(14) + 14

P = 11 + 11+ 14

P = 36 in.

Which is the height of the triangular prism?

• 6.2 cm

• 7.4 cm

• 11 cm

• 15.3 cm

Answer explanation

Remember that the height of a prism is the distance between the two matching faces. For a triangular prism, it is the length between the 2 triangles.

The diagram shows a tank partially filled with water. If the water fills 5/8 of the tank, find the depth of the water.

• 5 m

• 22.4 m

• 35.84 m

• 71.68 m

Answer explanation

If the tank is 5/8 filled, that means that its height is 5/8 of the full height of the tank.

(5/8)(height of prism) = depth of water

(5/8)(8) = depth of water

5 m = depth of water