find the surface area of a right cylinder with a diameter of 4cm and a height of 6cm. Round to the nearest hundredth.
Book answer is 100.53cm^2 I came up with 150.79cm^2
my work:
2rr(4)6)=150.79cm^2 What did I do wrong??
The book answer is correct.
There are two things you need to watch for:
1. The diameter is 4 cm means the radius is 2 cm.
For the formula 2πrh, you have substituted 4 for the radius, which therefore gave twice the value it is supposed to have, namely 75.40 sq.cm.
2. The other 25.13 comes from the area of the two ends, each given by πr². (Note: r=2 cm).
To find the surface area of a right cylinder, you need to consider two components: the top and bottom of the cylinder (which are circles) and the lateral surface area (which is a rectangle that wraps around the sides of the cylinder).
Let's break down the steps to calculate the surface area correctly:
1. Find the radius of the cylinder.
The diameter given is 4 cm, so the radius is half of that: 4 cm / 2 = 2 cm.
2. Calculate the area of the two circles (top and bottom).
The formula for the area of a circle is A = πr^2.
For each circle, it will be A = π(2 cm)^2 = 4π cm^2.
Since we have two circles, the combined area for both circles is 8π cm^2.
3. Calculate the area of the lateral surface.
The formula for the area of a rectangle is A = 2πrh, where r is the radius and h is the height.
For the lateral surface area, it will be A = 2π(2 cm)(6 cm) = 24π cm^2.
4. Add the areas of the circles and the lateral surface area.
8π cm^2 + 24π cm^2 = 32π cm^2.
Now, if we want to round to the nearest hundredth, we can use an approximation for π, which is 3.14.
32π cm^2 ≈ 32(3.14) cm^2 ≈ 100.48 cm^2.
Rounding to the nearest hundredth, the surface area of the right cylinder is approximately 100.48 cm^2.
It seems that the correct answer provided in the book is rounded to the nearest hundredth and matches our calculated value. Therefore, the book answer of 100.53 cm^2 seems to be the accurate one, not 150.79 cm^2.