Unit 4 review (PT and Volume)

Front

What is the formula to find the length of the diagonal in a three-dimensional figure?

Back

The formula is: \( d = \sqrt{l^2 + w^2 + h^2} \) where \( l \) is length, \( w \) is width, and \( h \) is height.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): \( c^2 = a^2 + b^2 \).

Front

If the area of one square is 369 and another is 81, how do you find the area of the missing square off of leg A?

Back

Use the Pythagorean theorem: \( A^2 + B^2 = C^2 \). Here, \( A^2 = 369 \) and \( B^2 = 81 \), so the missing area is \( C^2 = 369 + 81 = 450 \).

Front

What is the formula for the volume of a cone?

Back

The volume of a cone is given by the formula: \( V = \frac{1}{3} \pi r^2 h \) where \( r \) is the radius and \( h \) is the height.

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

Check if the square of the longest side equals the sum of the squares of the other two sides using the Pythagorean theorem.

Front

What is the area of a triangle with base 10 and height 5?

Back

The area is given by the formula: \( A = \frac{1}{2} \times base \times height = \frac{1}{2} \times 10 \times 5 = 25 \).

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Front

What is the formula for the surface area of a cylinder?

Back

The surface area of a cylinder is given by: \( SA = 2\pi r(h + r) \) where \( r \) is the radius and \( h \) is the height.

Front

What is the formula for the volume of a rectangular prism?

Back

The volume of a rectangular prism is given by: \( V = l \times w \times h \) where \( l \) is length, \( w \) is width, and \( h \) is height.

Front

What is the height of a cone if the volume is 150 cm³ and the radius is 5 cm?

Back

Using the volume formula \( V = \frac{1}{3} \pi r^2 h \), rearranging gives \( h = \frac{3V}{\pi r^2} \). Plugging in values gives \( h = \frac{3 \times 150}{\pi \times 5^2} \approx 7.64 \) cm.