Question

A pencil 8 in. long rests diagonally from lower base vertex to the upper vertex on a cube. Find the lateral area of the cube.

Answer 1

Step-by-step explanation:

LSA of a cube = 4a²

Therefore, 4×(8)² = 256

Answer 2

The lateral surface area of the cube is 85.33 inch².

Given:

• A pencil 8 inch long rests diagonally from the lower base vertex to the upper vertex on a cube.

To find:

• Find the lateral surface area of the cube.

Solution:

Formula to be used:

• The length of the diagonal from the lower vertex to the upper vertex is √3a, where 'a' is the length of the side of the cube.
• Lateral surface area of cube:4a²

Step 1:

Find the length of the side of the cube.

ATQ,

$\sqrt{3} a =8$

$\bf a = \frac{8}{ \sqrt{3} } \: inch$

Step 2:

Find the lateral surface area of the cube.

The lateral surface area of the cube is $4 {a}^{2}$

$LSA = 4 \times \frac{64}{3}$

$\bf LSA = 85.33 \: {inch}^{2}$

Thus,

Lateral surface area of cube is 85.33 inch².

Learn more:

1) Two cubes each of edge 12 cm are joined. The surface area of new cuboid is

(a) 140 cm (b) 1440 cm? (c) 144 cm

(d) 72 ...

https://brainly.in/question/28854999

2) A cubical box is 15 cm long and another cuboidal box is 25 cm long, 20 cm wide and 10 cm high.

(1) Which box has the sma...

https://brainly.in/question/11768553

#SPJ3