Math - Cylinders | Practice Hub

What is the surface area of a cylinder with a radius of 2 cm and a height of 10 cm?

40π cm2

32π cm2

56π cm2

48π cm2

36π cm2

Explanation

SAcylinder = 2πrh + 2πr2 = 2π(2)(10) + 2π(2)2 = 40π + 8π = 48π cm2

What is the surface area of a cylinder with a radius of 2 cm and a height of 10 cm?

40π cm2

32π cm2

56π cm2

48π cm2

36π cm2

Explanation

SAcylinder = 2πrh + 2πr2 = 2π(2)(10) + 2π(2)2 = 40π + 8π = 48π cm2

The volume of a cylinder is $81\pi$ . If the radius of the cylinder is , what is the surface area of the cylinder?

$72\pi$

$9\pi$

$27\pi$

$3\pi$

$81\pi$

Explanation

The volume of a cylinder is equal to:

$V=\pi r^2h$

Use this formula and the given radius to solve for the height.

$81\pi=\pi(3)^2h$

$81\pi=9\pi(h)$

Now that we know the height, we can solve for the surface area. The surface area of a cylinder is equal to the area of the two bases plus the area of the outer surface. The outer surface can be "unwrapped" to form a rectangle with a height equal to the cylinder height and a base equal to the circumference of the cylinder base. Add the areas of the two bases and this rectangle to find the total area.

$A=2A_{base}+A_{rec}$

$A=2\pi r^2+(2\pi r)(h)$

Use the radius and height to solve.

$A=2\pi (3)^2+2\pi (3)(9)$

$A=18\pi+54\pi$

$A=72\pi$

What is the surface area of a cylinder with a base diameter of and a height of ?

$36\pi in^{2}$

$14\pi in^{2}$

$66\pi in^{2}$

$48\pi in^{2}$

None of the answers

Explanation

Area of a circle $A=\pi r^{2}=\pi(\frac{d}{2})^{2}=\pi(\frac{6}{2})^{2}=\pi(3)^{2}=9\pi in^{2}$

Circumference of a circle $C=\pi d=6\pi in^{2}$

Surface area of a cylinder $SA=2A+hC=2(9\pi)+8(6\pi)=18\pi+48\pi=66\pi in^{2}$

What is the surface area of a cylinder with a base diameter of and a height of ?

$36\pi in^{2}$

$14\pi in^{2}$

$66\pi in^{2}$

$48\pi in^{2}$

None of the answers

Explanation

Area of a circle $A=\pi r^{2}=\pi(\frac{d}{2})^{2}=\pi(\frac{6}{2})^{2}=\pi(3)^{2}=9\pi in^{2}$

Circumference of a circle $C=\pi d=6\pi in^{2}$

Surface area of a cylinder $SA=2A+hC=2(9\pi)+8(6\pi)=18\pi+48\pi=66\pi in^{2}$

The volume of a cylinder is $81\pi$ . If the radius of the cylinder is , what is the surface area of the cylinder?

$72\pi$

$9\pi$

$27\pi$

$3\pi$

$81\pi$

Explanation

The volume of a cylinder is equal to:

$V=\pi r^2h$

Use this formula and the given radius to solve for the height.

$81\pi=\pi(3)^2h$

$81\pi=9\pi(h)$

$A=2A_{base}+A_{rec}$

$A=2\pi r^2+(2\pi r)(h)$

Use the radius and height to solve.

$A=2\pi (3)^2+2\pi (3)(9)$

$A=18\pi+54\pi$

$A=72\pi$

Find the surface area of the following cylinder.

Cylinder

$104 \pi m^2$

$114 \pi m^2$

$124 \pi m^2$

$94 \pi m^2$

$84 \pi m^2$

Explanation

The formula for the surface area of a cylinder is:

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

Where is the radius of the cylinder and is the height of the cylinder

Plugging in our values, we get:

$SA = 2\pi (4m)^2 + 2 \pi (4m)(9m)$

$SA = 104 \pi m^2$

Find the surface area of the following cylinder.

Cylinder

$252 \pi m^2$

$240 \pi m^2$

$260 \pi m^2$

$256 \pi m^2$

$246 \pi m^2$

Explanation

The formula for the surface area of a cylinder is:

$SA = lateral\ area + 2\cdot (base)$

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

where is the radius of the base and is the length of the height.

Plugging in our values, we get:

$SA = 2 \pi (7m) (11m) + 2 \pi (7m)^2$

$SA = 154 \pi m^2 + 98 \pi m^2 = 252 \pi m^2$

Calculate the volume of a cylinder with a height of six, and a base with a radius of three.

$54\pi$

$18\pi$

Explanation

The volume of a cylinder is give by the equation $\small V=\pi r^2h$ .

In this example, $\small h=6$ and $\small r=3$ .

$V=\pi(3)^2(6)$

$V=\pi(9)(6)=54\pi$

The base of a cylinder has an area of $9\pi$ and the cylinder has a height of . What is the surface area of this cylinder?

$90\pi$

$18\pi$

$72\pi$

Explanation

The standard equation for the surface area of a cylinder is

$SA=2\pi r^2+2\pi rh$

where denotes radius and denotes height. We've been given the height in the question, so all we're missing is the radius. However, we are able to find the radius from the area of the circle: