A right circular cone has a volume of \frac{1}{3} \pi cubic feet and a height of 9 feet. What is the radius, in feet, of the base of the cone?

A. \frac{1}{3}. Choice A is correct. The equation for the volume of a right circular cone is $V = \frac{1}{3} \pi r^2 h$. It's given that the volume of the right circular cone is $\frac{1}{3} \pi$ cubic feet and the height is 9 feet. Substituting these values for $V$ and $h$, respectively, gives $\frac{1}{3} \pi = \frac{1}{3} \pi r^2 (9)$. Dividing both sides of the equation by $\frac{1}{3} \pi$ gives $1 = r^2 (9)$. Dividing both sides of the equation by 9 gives $\frac{1}{9} = r^2$. Taking the square root of both sides results in two possible values for the radius, $\sqrt{\frac{1}{9}}$ or $-\sqrt{\frac{1}{9}}$. Since the radius can't have a negative value, that leaves $\sqrt{\frac{1}{9}}$ as the only possibility. Applying the quotient property of square roots, $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$, results in $r = \frac{\sqrt{1}}{\sqrt{9}}$, or $r = \frac{1}{3}$. Choices B and C are incorrect and may result from incorrectly evaluating $\sqrt{\frac{1}{9}}$. Choice D is incorrect and may result from solving $r^2 = 9$ instead of $r^2 = \frac{1}{9}$.

SAT Math skill page

SAT Area and Volume Practice

Choose the right formula, track units, and separate area from volume.

Practice area and volume in Dolphin SAT Practice questions

10-16 min practice time3 questions on pageGeometry

Practice time10-16 min

Question bank3 questions

Best forGeometry

What this tests

What to know for this SAT skill

Use area formulas for common shapes
Use volume formulas for prisms and cylinders
Track square and cubic units
Break composite figures into simpler shapes

Dolphin question bank

Practice your skill

Question 1 of 3Hard

A cube has a surface area of 54 square meters. What is the volume, in cubic meters, of the cube?

Show answer and solution

Correct answerB. 27

Solution walkthrough

The surface area of a cube with side length $s$ is equal to $6 s^{2}$ . Since the surface area is given as 54 square meters, the equation $54 = 6 s^{2}$ can be used to solve for $s$ .
Dividing both sides of the equation by 6 yields $9 = s^{2}$ . Taking the square root of both sides of this equation yields $3 = s$ and $- 3 = s$ .
Since the side length of a cube must be a positive value, $s = - 3$ can be discarded as a possible solution, leaving $s = 3$ . The volume of a cube with side length $s$ is equal to $s^{3}$ .
Therefore, the volume of this cube, in cubic meters, is $3^{3}$ , or 27.

Question 2 of 3Hard

The dimensions of a right rectangular prism are 4 inches by 5 inches by 6 inches. What is the surface area, in square inches, of the prism?

Show answer and solution

Correct answerD. 148

Solution walkthrough

The surface area is found by summing the area of each face.
A right rectangular prism consists of three pairs of congruent rectangles, so the surface area is found by multiplying the areas of three adjacent rectangles by 2 and adding these products.
For this prism, the surface area is equal to $2 (4 \cdot 5) + 2 (5 \cdot 6) + 2 (4 \cdot 6)$ , or $2 (20) + 2 (30) + 2 (24)$ , which is equal to 148.

Question 3 of 3Hard

A right circular cone has a volume of

\frac{1}{3} π c u bi c f ee t

and a height of 9 feet. What is the radius, in feet, of the base of the cone?

$\frac{1}{3}$
$\frac{1}{3}$
$3$
3

Show answer and solution

Correct answer $A . \frac{1}{3}$

Solution walkthrough

The equation for the volume of a right circular cone is $V = \frac{1}{3} π r^{2} h$ . It's given that the volume of the right circular cone is $\frac{1}{3} π$ cubic feet and the height is 9 feet.
Substituting these values for $V$ and $h$ , respectively, gives $\frac{1}{3} π = \frac{1}{3} π r^{2} (9)$ . Dividing both sides of the equation by $\frac{1}{3} π$ gives $1 = r^{2} (9)$ .
Dividing both sides of the equation by 9 gives $\frac{1}{9} = r^{2}$ . Taking the square root of both sides results in two possible values for the radius, $\frac{1}{9}$ or $- \frac{1}{9}$ .
Since the radius can't have a negative value, that leaves $\frac{1}{9}$ as the only possibility. Applying the quotient property of square roots, $\frac{a}{b} = \frac{a}{b}$ , results in $r = \frac{1}{9}$ , or $r = \frac{1}{3}$ .

Why the other choices miss

Choices B and C are incorrect and may result from incorrectly evaluating

\frac{1}{9}

. Choice D is incorrect and may result from solving

r^{2} = 9

instead of

r^{2} = \frac{1}{9}

Avoid these traps

Common mistakes on this skill

Using a perimeter formula for area

Perimeter measures boundary length, area measures a two-dimensional region, and volume measures three-dimensional space.

Forgetting squared or cubed units

Area uses square units and volume uses cubic units; the units are part of the result.

Study plan

How to practice this skill in Dolphin

Sketch and label the dimensions, including any hidden radius, height, or shared side.
Choose the formula that matches the requested measure rather than the pictured shape alone.
Substitute consistently converted dimensions and check the final units.

Practice area and volume in Dolphin SAT

Related practice

Build the surrounding skills

Skill cluster

Keep practicing SAT Math

FAQ

Questions about SAT Area and Volume Practice

How do scale factors affect area and volume?

A length scale factor k multiplies area by k^2 and volume by k^3.

Is the SAT formula sheet enough for these questions?

It supplies many formulas, but you still need to identify the correct dimensions and whether the question asks for area, surface area, or volume.