Question

Can someone please help me with this math problems

Answer 1

97.

Formulas for surface area and volume of a rectangular prism (this is a cube, which is a special kind of rectangular prism; the same formulas can be used for both types of figures):

S.A. = 2(wh + lw + lh), where w is the width, h is the height, and l is the length

V = lwh; likewise, w is width, h is height, and l is length

Our width, length, and height are as follows:

w = 8

l = 8

h = 8

Plug these values into each formula and solve.

S.A. = 2(wh + lw +lh)

S.A. = 2(8(8) + 8(8) + 8(8))

S.A. = 2(64 + 64 + 64)

S.A. = 2(192)

S.A. = 384

V = lwh

V = 8 * 8 * 8

V = 512

Answer: S.A. = 384 cm²; V = 512 cm³.

98.

This is also a rectangular prism, so the same formulas will be used.

Width, length, and height:

w = 2

l = 12

h = 3

S.A. = 2(wh + lw + lh)

S.A. = 2(2(3) + 12(2) + 12(3))

S.A. = 2(6 + 24 + 36)

S.A. = 2(66)

S.A. = 132

V = lwh

V = 12 * 2 * 3

V = 72

Answer: S.A. = 132 in²; V = 72 in³.

99.

Formulas for S.A. and V of a right cylinder:

S.A. = 2πrh + 2πr², where r is the radius and h is the height

V = πr²h; r is the radius and h is the height

Radius and height:

r = 7

h = 3

S.A. = 2πrh + 2πr²

S.A. = 2π(7)(3) + 2π(7)²

S.A. = 42π + 2π49

S.A. = 42π + 98π

S.A. = 140π or approx. 440

V = πr²h

V = π(7)²(3)

V = π49(3)

V = 147π or approx. 462

Answer: S.A. ≈ 440 cm²; V ≈ 462 cm³.

100.

Same formulas as above. Notice we're given the diameter of the cylinder, however, rather than the radius. The radius is half the diameter, so the radius is 4.5 mm.

Radius and height:

r = 4.5

h = 13

S.A. = 2πrh + 2πr²

S.A. = 2π(4.5)(13) + 2π(4.5)²

S.A. = 117π + 2π20.25

S.A. = 117π + 40.5π

S.A. = 157.5π or approx. 495

V = πr²h

V = π(4.5)²(13)

V = π20.25(13)

V = 263.25π or approx. 827

Answer: S.A. ≈ 495 mm²; V ≈ 827 mm³.