Question

1. the surface area of the cylinder shown is :

a. 147 cm²
b. 175 cm²
c. 266 cm²
d. 294 cm²

1. which 8 - cube arrangement has the least surface area?
2. the formula needed to calculate the surface area of a lidless glass jar with a radius of r and height of h is:

a. s.a. = 2πr² + 2πrh
b. s.a. = πr² + πrh
c. s.a. = 2πrh
d. s.a. = πr² + 2πrh
determine the surface area of the object shown if the side length of each cube is 1 cm.
20 cm²
26 cm²
28 cm²
42 cm²

Explanation:

6.

Step1: Recall surface - area formula for cylinder

The surface - area formula of a cylinder is $S.A. = 2\pi r^{2}+2\pi rh$, where $r$ is the radius and $h$ is the height. Given $r = 6\div2=3$ cm and $h = 12.6$ cm.
$S.A.=2\pi r^{2}+2\pi rh=2\pi\times3^{2}+2\pi\times3\times12.6$

Step2: Calculate each part

$2\pi\times3^{2}=2\pi\times9 = 18\pi$ and $2\pi\times3\times12.6 = 75.6\pi$.
$S.A.=(18 + 75.6)\pi=93.6\pi\approx93.6\times3.14 = 293.904\approx294$ $cm^{2}$

Let the side - length of each cube be $a$.

Step1: Analyze option A

For a $2\times2\times2$ cube (formed by 8 small cubes), the side - length of the large cube is $2a$. The surface area $S_{A}=6\times(2a)^{2}=24a^{2}$.

Step2: Analyze option B

For a $1\times2\times4$ arrangement of cubes, $S_{B}=2(1\times2 + 1\times4+2\times4)a^{2}=2(2 + 4 + 8)a^{2}=28a^{2}$.

Step3: Analyze option C

For a $1\times1\times8$ arrangement of cubes, $S_{C}=2(1\times1+1\times8 + 1\times8)a^{2}=2(1+8 + 8)a^{2}=34a^{2}$.
The $2\times2\times2$ cube (option A) has the least surface area.

A lidless glass jar is a cylinder with one base. The surface - area formula of a cylinder is $S.A. = 2\pi r^{2}+2\pi rh$ (with two bases). For a lidless cylinder, we subtract the area of one base. So the surface - area formula is $S.A.=\pi r^{2}+2\pi rh$.

Answer:

D. $294$ $cm^{2}$

7.