Afew math questions ! 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

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

C

C

C

D

Step-by-step 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: 414,377,008

step-by-step explanation:

just multiply it