Let's break down the questions in the images:

Question 1:

• We have a rectangular box with dimensions: 6 cm, 5 cm, and 7 cm.

  • a) To find the surface area, we can use the formula for the surface area of a rectangular box: $\text{Surface Area} = 2lw + 2lh + 2wh$ where $l = 6$, $w = 5$, and $h = 7$ cm.

  • b) To find the volume, we use the formula for the volume of a rectangular box: $\text{Volume} = l \times w \times h$

Question 2:

• A sphere with a radius of 12 cm.

  • a) The surface area of a sphere is given by the formula: $\text{Surface Area} = 4\pi r^2$ where $r = 12$ cm.

  • b) The volume of a sphere is given by the formula: $\text{Volume} = \frac{4}{3}\pi r^3$

Question 3:

• A campus quadrangle with dimensions 40 m by 30 m.
  • The buildings are positioned at the corners of a triangle, and we need to find the length of the sidewalks (gold lines) between the Library, Chemistry, and Humanities buildings. We can apply the distance formula to calculate the length of the sidewalks, given the coordinates for the locations of the buildings.
  • The distance formula is: $\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Would you like me to solve these step by step for you? Let me know if you'd like more details!