2. A cube has a side length of x feet. Which expression represents the surface area of the cube?
4x square units
24x square units
x'2 square units
6x'2 square units ***
3. Find the surface area of the cylinder that has a height of 15 cm and a diameter of 2 cm. Use 3.14 for pi.
a. 100.48 cm'2 ***
b. 97.43 cm'2
c. 36.28 cm'2
d. 33.14 cm'2
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To find the surface area of a cube with a side length of x feet, you need to find the area of all six sides and then sum them up.
Since a cube has six square faces, each side has an area of x^2 square units. Therefore, the total surface area of the cube is 6 times the area of each side.
The correct expression representing the surface area of the cube is 6x^2 square units.
Now, to find the surface area of a cylinder, you need to calculate the sum of the areas of its two circular bases and its curved surface.
The formula for the surface area of a cylinder is:
Surface Area = 2πr^2 + 2πrh
Given that the cylinder has a height of 15 cm and a diameter of 2 cm, we can calculate the radius (r) and height (h) of the cylinder.
The radius is half the diameter, so r = 2 cm / 2 = 1 cm.
The height is given as 15 cm.
Now, substitute the values into the formula for surface area:
Surface Area = 2π(1 cm)^2 + 2π(1 cm)(15 cm)
= 2π(1 cm)^2 + 2π(1 cm)(15 cm)
= 2π(1 cm)^2 + 2π(15 cm)
= 2π + 30π
= 32π cm^2
Since the value of pi (π) is given as 3.14, we can approximate the surface area:
Surface Area ≈ 32(3.14) cm^2
≈ 100.48 cm^2
Therefore, the correct answer is a. 100.48 cm^2.