Question

A FEW MATH QUESTIONS ! PLEASE EXPLAIN ANSWERS ! (:

1) A cone has a base area of 20 in² and a lateral area which is 2½ times bigger than the base area. The surface area of the cone is _____ in².

50
55
70
75

2) The dimensions of a rectangular prism are the same as a Pythagorean triangle with legs of 12 and 16. The volume of the prism is

192.
768.
3840.
5860.

3) A cone has a volume of 12 ft3. The volume of a cylinder with the same height and a congruent base is _____ ft3.

12
24
36
48

4) A triangular pyramid has a volume of 9 ft³. If all its dimensions are doubled, the volume of the new pyramid will be _____ ft³.

18
36
54
72

Answer 1

C

C

C

D

Explanation:

One

LA (Lateral Area) = 2.5 * BA (Base Area)

LA = 2.5 * 20

LA = 50 in^2

But the surface area = Lateral Area + Base

LA = 50

Base = 20

Total Surface Area = 70

Answer C

Two

The hypotenuse of the triangle is sqrt(a^2 + b^2)

a = 12

b = 16

c = ?

c =sqrt(12^2 + 16^2)

c = sqrt(144 + 256)

c = sqrt(400)

c = 20

Volume of rectangular Prism= L*W*H

L = 20

W = 12

H = 16

V = 20 * 12 * 16

V = 3840

C <<<<< answer

Three

V_cone = 1/3 B * H

3 * V_cone = BH

V_cylinder= B * H Equate equals to equals.

V_cylinder =3 * Cone

The cylinder has 3 times the volume of the cone.

V_cylinder = 3 * 12ft^3

V_cylinder = 36 ft^3

Answer C

Four

B = 1/2 * b * h of the triangle

Volume of pyramid = 1/3 * 1/2 * b * h * H where H is the height of the Pyramid.

Volume of Pyramid = 1/6 * b*h * H Now b*h*H are each doubled.

Volume of Pyramid = 1/6 * (2*b)(2*h)(2*H)

Volume of New Pyramid = 1/6 * 8 (b * h * H)

The volume has increased by a factor of 8.

If the smaller pyramid was 9 then the new larger one is 8*9 = 72

D <<<< answer

Answer 2

answers

1) 70

2) 3,840

3) 24

4) 72

Explanation

Q1

The surface area of a cone is given by;

S.A = 2Πrl + Πr²

Where r is the radius of the base and l is the lateral height.

Πr² = area of the base = 20 in²

2Πrl = Area of the lateral surface

= 2.5 × 20

= 50

Area of the cone = 50 + 20

= 70 in²

Q2

The sides of the Pythagorean triangle with legs of 12 and 16.

The 3rd side will be;

c = √(12² + 16²)

= √400 = 20

Volume = 12 × 16 × 20

= 3,840

Q3

The volume of a cone is given by;

volume = 1/3 Π r² h

This shows that the volume of a cone is a third the volume of the cylinder.

∴ Volume of the cylinder = 12 × 3

= 24 ft³

Q4

The volume of any regular figure is;

Volume = base area × height

When the dimensions area usually 3. Let these dimensions be x, y and z.

∴ volume = x × y × z = 9

Doubling the dimensions;

Volume = 2x × 2y × 2z = 2 × 2 × 2 × 9

= 8 × xyz = 8 × 9

= 72 ft²