Question

1. a pizza is 14 inches in diameter.how much pizza can fit in the pizza pan?8. emma has a notebook that is 9 inches long, 6 inches wide, and 1.5 inches tall.how much space will the book take up on the shelf?9. a water tank is shaped like a cylinder with a height of 10 feet and a radius of 4 feet.what is the volume of the tank?10. jake wants to carpet his rectangular room that is 14 feet by 11 feet.how much carpet is needed to cover the floor?11. a playground is in the shape of a triangle with sides of 8 meters, 7 meters, and 6 meters.how much fence is needed to surround the playground?12. a soda can has a height of 5 inches and a radius of 1.5 inches.how much aluminum is needed to make the can?

Explanation:

Problem 7

Step1: Find pizza radius

Radius $r = \frac{14}{2} = 7$ inches

Step2: Calculate area of pizza

Area $A = \pi r^2 = \pi (7)^2 = 49\pi \approx 153.94$ square inches

Problem 8

Step1: Apply rectangular volume formula

Volume $V = l \times w \times h$

Step2: Substitute values and compute

$V = 9 \times 6 \times 1.5 = 81$ cubic inches

Problem 9

Step1: Apply cylinder volume formula

Volume $V = \pi r^2 h$

Step2: Substitute values and compute

$V = \pi (4)^2 (10) = 160\pi \approx 502.65$ cubic feet

Problem 10

Step1: Apply rectangle area formula

Area $A = l \times w$

Step2: Substitute values and compute

$A = 14 \times 11 = 154$ square feet

Problem 11

Step1: Calculate perimeter of triangle

Perimeter $P = a + b + c$

Step2: Substitute values and compute

$P = 8 + 7 + 6 = 21$ meters

Problem 12

Step1: Apply total surface area formula for cylinder

Surface Area $SA = 2\pi r^2 + 2\pi r h$

Step2: Substitute values and compute

$SA = 2\pi (1.5)^2 + 2\pi (1.5)(5) = 4.5\pi + 15\pi = 19.5\pi \approx 61.26$ square inches

Answer:

1. $\boldsymbol{49\pi}$ (or ~153.94) square inches
2. $\boldsymbol{81}$ cubic inches
3. $\boldsymbol{160\pi}$ (or ~502.65) cubic feet
4. $\boldsymbol{154}$ square feet
5. $\boldsymbol{21}$ meters
6. $\boldsymbol{19.5\pi}$ (or ~61.26) square inches