7.G.B.6 Math Practice Questions — Sports Academy Games

Practice playeasy

Find the volume of a cone with radius $3$ and height $5$ . Use $\pi = 3$ .

$V = \dfrac{1}{3}\pi r^2 h = \dfrac{1}{3} \times 3 \times 9 \times 5 = 45$ .

Practice playhard

A rectangular prism has volume $72$ cubic centimeters and height $4$ centimeters. The length is twice the width. What is the width, in centimeters?

$V = \ell w h$ and $\ell = 2w$ , so $72 = (2w)(w)(4) = 8w^2$ . Then $w^2 = 9$ and $w = 3\text{ cm}\textsf{.}$

Practice playmedium

A shipping company uses closed rectangular cartons that measure $6$ centimeters by $4$ centimeters by $5$ centimeters. What is the total exterior surface area, in square centimeters, of one carton?

Use $SA = 2lw + 2lh + 2wh$ with $l = 6$ , $w = 4$ , and $h = 5$ . Then $SA = 2(6)(4) + 2(6)(5) + 2(4)(5) = 48 + 60 + 40 = 148$ square centimeters.

Practice playeasy

A cylinder has radius $2$ and height $4$ . Using $\pi = 3$ , what is its volume?

$V = \pi r^2 h = 3 \times 4 \times 4 = 48$ .

Practice playeasy

Find the volume of a cylinder with radius $3$ and height $2$ . Use $\pi = 3$ .

$V = \pi r^{2} h = 3 \times 9 \times 2 = 54$ .

Practice playhard

A rectangular prism has volume $160$ cubic inches and height $5$ inches. The length is twice the width. What is the length, in inches?

$V = \ell w h$ and $\ell = 2w$ , so $160 = (2w)(w)(5) = 10w^2$ . Then $w^2 = 16$ , so $w = 4$ and $\ell = 8\text{ in}\textsf{.}$

Practice playmedium

A gardener builds an open-top planter box in the shape of a rectangular prism. The inside measures $8$ inches long, $3$ inches wide, and $4$ inches deep, and the box has no lid. What is the exterior surface area, in square inches, of the planter?

Use $SA = 2lw + 2lh + 2wh$ with $l = 8$ , $w = 3$ , and $h = 4$ . Then $SA = 2(8)(3) + 2(8)(4) + 2(3)(4) = 48 + 64 + 24 = 136$ for a closed box. The open top removes one $8 \times 3$ face, so subtract $24$ to get $136 - 24 = 112$ square inches.