Question

Kenny plans to paint the mailbox below. If it costs $3.50 per quart of paint and one quart will cover 10 square feet, how many quarts will Kenny need to buy? What will it cost?

Answer 1

Kenny need to buy 4 quarts.

It cost $14.

Solution:

The mailbox is splitted into two shapes.

One is rectangle and the other is hemisphere.

Length of the rectangle = 2.4 ft

Width of the rectangle = 1.5 ft

Height of the rectangle = 3 ft

Surface area of the given rectangle

                   = 2(lw + wh + lh) – lw

                   = 2(2.4 × 1.5 + 1.5 × 3 + 2.4 × 3) – (2.4 × 1.5)

                   = 2(3.6 + 4.5 + 7.2) – 3.6

                   = 2(15.3) – 3.6

                   = 27

Surface area of the given rectangle = 27 square feet

Radius of the hemisphere = 1.2 ft

Curved surface area of hemisphere

                  = $2\pi r^2$

                  $=2 \times 3.14 \times 1.2 \times 1.2$

                 = 9.0432 square feet

Curved surface area of hemisphere = 9.0432 square feet                                      

Total surface area of the mailbox  = 27 + 9.0432

                                                         = 36.0432 square feet

To find how many quarts are needed to cover the mailbox.

1 Quart covers = 10 square feet

36.0432 sq. ft = 36.0432 ÷ 10

                       = 3.60432 quarts

                       ≈ 4 quarts (approximately)

Hence Kenny need to buy 4 quarts.

Cost of 1 quart = $3.50

Cost of 4 quart = 4 × 3.50

                         = 14

Hence it cost $14.