3-Dimensional Geometry - GED Math

Card 1 of 800

0

Didn't Know

0

Didn't Know

Knew It

0

1 of 2019 left

Question

Let $\pi = 3.14$

If a cylinder has a height of 7in and a radius of 4in, find the volume.

Tap to reveal answer

Answer

To find the volume of a cylinder, we will use the following formula:

$V = \pi r^2 h$

where r is the radius and h is the height of the cylinder.

We know $\pi=3.14$ .

We know the radius of the cylinder is 4in.

We know the height of the cylinder is 7in.

Now, we can substitute. We get

$V = 3.14 \cdot (4\text{in})^2 \cdot 7\text{in}$

$V = 3.14 \cdot 16\text{in}^2 \cdot 7\text{in}$

$V = 3.14 \cdot 112\text{in}^3$

$V = 351.68\text{in}^3$

← Didn't Know|Knew It →

Question

Find the volume of a cylinder with a base area of 15, and a height of 10.

Tap to reveal answer

Answer

Write the volume formula for the cylinder. The area of the base is a circle or $\pi r^2$ .

$V =\pi r^2h =Bh$

Substitute the base and height.

The volume is:

← Didn't Know|Knew It →

Question

Let $\pi = 3.14$ .

Find the volume of a cylinder with a radius of 4cm and a height of 6cm.

Tap to reveal answer

Answer

To find the volume of a cylinder, we will use the following formula:

$V = \pi r^2 h$

where r is the radius and h is the height of the cylinder.

Now, we know $\pi = 3.14$ . We know the radius of the cylinder is 4cm. We know the height of the cylinder is 6cm. So, we substitute. We get

$V = 3.14 \cdot (4\text{cm})^2 \cdot 6\text{cm}$

$V = 3.14 \cdot 16\text{cm}^2 \cdot 6\text{cm}$

$V = 3.14 \cdot 96\text{cm}^3$

$V = 301.44\text{cm}^3$

← Didn't Know|Knew It →

Question

Find the volume of a cylinder with a radius of 10, and a height of 20.

Tap to reveal answer

Answer

Write the formula for the volume of a cylinder.

$V= \pi r^2 h$

Substitute the radius and height.

$V= \pi (10)^2 (20) = \pi (100) (20)$

The answer is: $2000\pi$

← Didn't Know|Knew It →

Question

Find the volume of a cylinder with a radius of 5 and a height of 12.

Tap to reveal answer

Answer

Write the formula for the volume of a cylinder.

$V= \pi r^2 h$

Substitute the dimensions.

$V= \pi (5)^2 (12) = \pi (25) (12 )= 300 \pi$

The answer is: $300 \pi$

← Didn't Know|Knew It →

Question

How many edges and vertices are found on a square pyramid?

Tap to reveal answer

Answer

The base of a square pyramid is, as the name suggests, a square which has edges and vertices. The vertices of the square each have edges that meet at a single point, adding an additional vertex and additional edges. Together, a square pyramid has edges and vertices.

← Didn't Know|Knew It →

Question

How many vertices does an octagonal pyramid have?

Tap to reveal answer

Answer

An octagonal pyramid has a base with eight vertices, each of which is a vertex of the pyramid. There is one more vertex, or the apex, which is connected to each of the vertices of the base by an edge. Nine is the correct choice.

← Didn't Know|Knew It →

Question

A circular swimming pool at an apartment complex has diameter 18 meters and depth 2.5 meters throughout.

The apartment manager needs to get the interior of the swimming pool painted. The paint she wants to use covers 40 square meters per can. How many cans of paint will she need to purchase?

You may use 3.14 for $\pi$ .

Tap to reveal answer

Answer

The pool can be seen as a cylinder with depth (or height) 2.5 meters and a base with diameter 18 meters - and radius half this, or 9 meters.

The bottom of the pool - the base of the cylinder - is a circle with radius 9 meters, so its area is

$B = \pi r ^{2} = 3.14 \cdot 9 \cdot 9 = 254.34$ square meters.

Its side - the lateral face of the cylinder - has area

$LA = 2 \pi r h = 2 \cdot 3.14 \cdot 18 \cdot 2.5 = 141.3$ square meters.

Their sum - the total area to be painted - is square feet. Since one can of paint covers 40 square meters, divide:

$395.64 \div 40 \approx 9.891$

Nine cans of paint and part of a tenth will be required, so the correct response is ten.

← Didn't Know|Knew It →

Question

A regular icosahedron has twenty congruent faces, each of which is an equilateral triangle.

A given regular icosahedron has edges of length two inches. Give the total surface area of the icosahedron.

Tap to reveal answer

Answer

The area of an equilateral triangle is given by the formula

$A = \frac{s^{2}\sqrt{3}}{4}$ .

Since there are twenty equilateral triangles that comprise the surface of the icosahedron, the total surface area is

$SA = 20 A = 20 \cdot \frac{s^{2}\sqrt{3}}{4} = 5 s^{2}\sqrt{3}$ .

Substitute :

$SA = 5 \cdot 2^{2}\sqrt{3} = 5 \cdot 4 \sqrt{3} = 20 \sqrt{3}$ square inches.

← Didn't Know|Knew It →

Question

A regular octahedron has eight congruent faces, each of which is an equilateral triangle.

A given octahedron has edges of length three inches. Give the total surface area of the octahedron.

Tap to reveal answer

Answer

The area of an equilateral triangle is given by the formula

$A = \frac{s^{2}\sqrt{3}}{4}$ .

Since there are eight equilateral triangles that comprise the surface of the octahedron, the total surface area is

$SA = 8 A = 8 \cdot \frac{s^{2}\sqrt{3}}{4} = 2 s^{2}\sqrt{3}$ .

Substitute :

$SA =2 \cdot 3^{2}\sqrt{3} = 18 \sqrt{3}$ square inches.

← Didn't Know|Knew It →

Question

A regular tetrahedron has four congruent faces, each of which is an equilateral triangle.

A given tetrahedron has edges of length five inches. Give the total surface area of the tetrahedron.

Tap to reveal answer

Answer

The area of an equilateral triangle is given by the formula

$A = \frac{s^{2}\sqrt{3}}{4}$ .

Since there are four equilateral triangles that comprise the surface of the tetrahedron, the total surface area is

$SA = 4 A = 4 \cdot \frac{s^{2}\sqrt{3}}{4} = s^{2}\sqrt{3}$ .

Substitute :

$SA = 5^{2}\sqrt{3} = 25 \sqrt{3}$ square inches.

← Didn't Know|Knew It →

Question

A water tank takes the shape of a sphere whose exterior has radius 24 feet; the tank is six inches thick throughout. To the nearest hundred, give the surface area of the interior of the tank in square feet.

Use 3.14 for $\pi$ .

Tap to reveal answer

Answer

Six inches is equal to 0.5 feet, so the radius of the interior of the tank is

feet.

The surface area of the interior of the tank can be calculated using the formula

$SA = 4 \pi r^{2}$

$SA \approx 4 \cdot 3.14 \cdot 23.5 ^{2} \approx 6,936$ ,

which rounds to 6,900 square feet.

← Didn't Know|Knew It →

Question

A water tank takes the shape of a closed cylinder whose exterior has a height of 40 feet and a base with radius 15 feet; the tank is three inches thick throughout. To the nearest hundred, give the surface area of the interior of the tank in square feet.

Use 3.14 for $\pi$ .

Tap to reveal answer

Answer

Three inches is equal to 0.25 feet, so the height of the interior of the tank is

$40 - 2 \times 0.25 = 39.5$ feet.

The radius of the interior of the tank is

feet.

The surface area of the interior of the tank can be determined by using this formula:

$SA = 2 \pi r (r + h)$

$SA = 2 \cdot 3.14 \cdot 14.75 (14.75 + 39.5)$

$SA \approx 2 \cdot 3.14 \cdot 14.75 \cdot 54.25\approx 5,025$ ,

which rounds to 5,000 square feet.

← Didn't Know|Knew It →

Question

Give the total surface area of the above cone to the nearest square meter.

Tap to reveal answer

Answer

The base is a circle with radius , and its area can be calculated using the area formula for a circle:

$B= \pi r^{2} = \pi \times 4^{2} \approx 3.14 \times 16 = 50.24$ square meters.

To find the lateral area, we need the slant height of the cone. This can be found by way of the Pythagorean Theorem. Treating the height and the radius as the legs and slant height as the hypotenuse, calculate:

$l^{2} = h^{2} + r^{2}$

$l^{2} = 10^{2} + 4^{2} = 100 + 16 = 116$

$l = \sqrt{116} \approx 10.77$ meters.

The formula for the lateral area can be applied now:

$LA = \pi r l \approx 3.14 \cdot 4 \cdot 10.77 \approx 135.34$

Add the base and the lateral area to obtain the total surface area:

$SA = B + LA \approx 50.24 + 135.34 \approx 185.58$ .

This rounds to 186 square meters.

← Didn't Know|Knew It →

Question

Above is a diagram of a conic tank that holds a city's water supply.

The city wishes to completely repaint the exterior of the tank - sides and base. The paint it wants to use covers 40 square meters per gallon. Also, to save money, the city buys the paint in multiples of 25 gallons.

How many gallons will the city purchase in order to paint the tower?

Tap to reveal answer

Answer

The surface area of a cone with radius and slant height is calculated using the formula $S = \pi r^{2} + \pi r l$ .

Substitute 35 for and 100 for to find the surface area in square meters:

$S = \pi \cdot 35^{2} + \pi \cdot 35 \cdot 100$

$\approx 3.14 \cdot 1,225 + 3.14\cdot 35 \cdot 100$

$\approx 3,848 + 10,996$

$\approx 14,844$ square meters.

The paint covers 40 square meters per gallon, so the city needs

$14,844 \div 40 =371.1$ gallons of paint.

Since the city buys the paint in multiples of 25 gallons, it will need to buy the next-highest multiple of 25, or 375 gallons.

← Didn't Know|Knew It →

Question

A cube has a height of 9cm. Find the surface area.

Tap to reveal answer

Answer

To find the surface area of a cube, we will use the following formula:

$SA = 6 \cdot l \cdot w$

where l is the length, and w is the width of the cube.

Now, we know the height of the cube is 9cm. Because it is a cube, all lengths, widths, and heights are the same. Therefore, the length and the width are also 9cm.

Knowing this, we can substitute into the formula. We get

$SA = 6 \cdot 9\text{cm} \cdot 9\text{cm}$

$SA = 6 \cdot 81\text{cm}^2$

$SA = 486\text{cm}^2$

← Didn't Know|Knew It →

Question

A sphere has a radius of 7in. Find the surface area.

Tap to reveal answer

Answer

To find the surface area of a sphere, we will use the following formula:

$SA = 4 \cdot \pi \cdot r^2$

where r is the radius of the sphere.

Now, we know the radius of the sphere is 7in.

So, we can substitute into the formula. We get

$SA = 4 \cdot \pi \cdot (7\text{in})^2$

$SA = 4 \cdot \pi \cdot 49\text{in}^2$

$SA = 196\text{in}^2 \cdot \pi$

$SA = 196\pi \text{ in}^2$

← Didn't Know|Knew It →

Question

Find the surface area of a cube with a length of 12in.

Tap to reveal answer

Answer

To find the surface area of a cube, we will use the following formula:

$SA = 6 \cdot l \cdot w$

where l is the length, and w is the width of the cube.

Now, we know the length of the cube is 12in. Because it is a cube, all sides are equal. Therefore, the width is also 12in. So, we can substitute. We get

$SA = 6 \cdot 12\text{in} \cdot 12\text{in}$

$SA = 6 \cdot 144\text{in}^2$

$SA = 864\text{in}^2$

← Didn't Know|Knew It →

Question

A cube has a height of 8cm. Find the surface area.

Tap to reveal answer

Answer

To find the surface area of a cube, we will use the following formula:

$SA = 6 \cdot l \cdot w$

where l is the length, and w is the width of the cube.

Now, we know the height of the cube is 8cm. Because it is a cube, all lengths, widths, and heights are the same. Therefore, the length and the width are also 8cm.

Knowing this, we can substitute into the formula. We get

$SA = 6 \cdot 8\text{cm} \cdot 8\text{cm}$

$SA = 6 \cdot 64\text{cm}^2$

$SA = 384\text{cm}^2$

← Didn't Know|Knew It →

Question

A sphere has a radius of 5in. Find the surface area.

Tap to reveal answer

Answer

To find the surface area of a sphere, we will use the following formula:

$SA = 4 \cdot \pi \cdot r^2$

where r is the radius of the sphere.

Now, we know the radius of the sphere is 5in.

So, we can substitute into the formula. We get

$SA = 4 \cdot \pi \cdot (5\text{in})^2$

$SA = 4 \cdot \pi \cdot 25\text{in}^2$

$SA = 100\text{in}^2 \cdot \pi$

$SA = 100\pi \text{ in}^2$

← Didn't Know|Knew It →

0

Knew It