SAT MAth Practice questions – all topics
- Geometry and Trigonometry Weightage: 15% Questions: 5-7
- Area and volume
- Lines, angles, and triangles
- Right triangles and trigonometry
- Circles
SAT MAth and English – full syllabus practice tests
Question Medium
Oocytes are a type of cell that can be modeled as a sphere. The table shows the surface area, in square micrometers \(\left(\mu \mathrm{m}^2\right)\), and volume, in cubic micrometers \(\left(\mu \mathrm{m}^3\right)\), based on the average radius for oocytes at the same stage of development in four types of mammals.
(The surface area of a sphere with a radius of \(r\) is \(4 \pi r^2\), and the volume of a sphere with a radius of \(r\) is equal to \(\frac{4}{3} \pi r^3\).
Based on the information in the table, what is the average radius, in micrometers, of a hamster oocyte?
A) 68.4
B) 20.7
C) 14.2
D) 11.7
▶️Answer/Explanation
Ans:D
To find the average radius of a hamster oocyte, we use the given surface area for the hamster:
Surface area of hamster oocyte: \(1,720.2 \, \mu \text{m}^2\)
The surface area \(A\) of a sphere is given by the formula:
\[
A = 4\pi r^2
\]
Rearrange to solve for \(r\):
\[
r^2 = \frac{A}{4\pi}
\]
\[
r = \sqrt{\frac{A}{4\pi}}
\]
Substitute the given surface area:
\[
r = \sqrt{\frac{1,720.2}{4\pi}}
\]
Calculate the value:
\[
r = \sqrt{\frac{1,720.2}{4 \times 3.14159}} = \sqrt{\frac{1,720.2}{12.56636}} \approx \sqrt{136.897} \approx 11.7
\]
Question medium
In the figure shown, ABCD is a parallelogram and EBFD is a square. The area of ABCD is 112 square meters \((m^2)\), and the area of EBFD is 64 \(m^2\). What is the length, in meters, of line segment AE ?
A) 6
B) 8
C) 14
D) 23
▶️Answer/Explanation
A) 6
$\text{Area of parallelogram}= \text{AD}\times \text{BE}$
$\text{Area of Square}= \text{DE}\times \text{BE}$ Since, in Square all sides are equal .
$\text{Area of Square}=64$
$\text{DE}^2~\text{or}~\text{BE}^2=64\Rightarrow 8$
Now, $\text{Area of parallelogram}=112$
$112= \text{AD}\times \text{BE}$
$\text{AD}=\frac{112}{8}\Rightarrow 14$
$\text{AD}=\rm{AE+ED}$ And DE=8
So, AE= 6 m
Question Medium
A right circular cylinder has a height of 6 inches. The radius of the base of the cylinder is 5 inches. What is the volume, in cubic inches, of the cylinder?
A. 10\(\pi \)
B. 30\(\pi \)
C. 50\(\pi \)
D. 150\(\pi \)
▶️Answer/Explanation
Ans: D
The volume \(V\) of a right circular cylinder is given by the formula:
\[V = \pi r^2 h\]
where \(r\) is the radius of the base and \(h\) is the height of the cylinder.
Given that the radius \(r\) is \(5\) inches and the height \(h\) is \(6\) inches,
\[V = \pi (5)^2 (6)\]
\[V = \pi (25)(6)\]
\[V = 150\pi\]
So, the volume of the cylinder is \(150\pi\) cubic inches.
Question Medium
The area of a rectangular region is increasing at a rate of 20 square feet per hour. Which of the following is closest to this rate in square meters per minute? (Use 1 meter = 3.28 feet.)
A. 0.03
B. 0.10
C. 1.09
D. 2.03
▶️Answer/Explanation
Ans: A
Step 1: Convert square feet per hour to square feet per minute
Given:
\[ 20 \text{ square feet per hour} \]
Since there are 60 minutes in an hour, we convert square feet per hour to square feet per minute by dividing by 60:
\[ 20 \text{ square feet per hour} \times \frac{1 \text{ hour}}{60 \text{ minutes}} = \frac{20}{60} \text{ square feet per minute} = \frac{1}{3} \text{ square feet per minute} \]
Step 2: Convert square feet to square meters
The conversion factor is:
\[ 1 \text{ meter} = 3.28 \text{ feet} \]
Therefore, \(1 \text{ square meter} = (3.28 \text{ feet})^2 = 10.7584 \text{ square feet}\)
To convert from square feet to square meters:
\[ 1 \text{ square foot} = \frac{1 \text{ square meter}}{10.7584 \text{ square feet}} = \frac{1}{10.7584} \text{ square meters} \]
Now, convert \(\frac{1}{3}\) square feet per minute to square meters per minute:
\[ \frac{1}{3} \text{ square feet per minute} \times \frac{1 \text{ square meter}}{10.7584 \text{ square feet}} = \frac{1}{3} \times \frac{1}{10.7584} \text{ square meters per minute} \]
Simplify the calculation:
\[ \frac{1}{3} \times \frac{1}{10.7584} = \frac{1}{3 \times 10.7584} = \frac{1}{32.2752} \approx 0.031 \text{ square meters per minute} \]
The closest answer is:
\[ \boxed{0.03} \]
Question Medium
The volume of the right triangular prism shown is 96 cubic centimeters \(\left(\mathrm{cm}^3\right)\). What is the area, in \(\mathrm{cm}^2\), of one of the triangular bases of the prism?
A) 4
B) 8
C) 16
D) 42
▶️Answer/Explanation
Ans:B
The volume \( V \) of a prism is given by the formula:
\[ V = \text{Base Area} \times \text{Height} \]
where the height is the length between the two triangular bases, which in this case is 12 cm.
\[ V = 96 \, \text{cm}^3 \]
\[ \text{Height} = 12 \, \text{cm} \]
\[ \text{Base Area} = \frac{V}{\text{Height}} \]
\[ \text{Base Area} = \frac{96 \, \text{cm}^3}{12 \, \text{cm}} \]
\[ \text{Base Area} = 8 \, \text{cm}^2 \]