Geometry problem, please help!!

Question

Answer 1

10-8

Surface area of sphere

Volume of sphere

Whre " r " is radius of sphere.

Given that volume of the sphere

To find surface area of the sphere substitute r = 2" in

Option H is correct answer.

Answer 2

2) Volume of the cone

Volume of the cone

Diameter(d) = 2* radius(r)

r = d/2

Let's check the each of possibilities.

A) d = 1inche then r = 1/2 inches. and h = 18inches

Substitute r, h values in

B) d = 6inches , h = 6inches

r = 6/2 = 3inches

Substitute r, h values in

C) d= 3inches, h = 6inches

r = 3/2inches

Substitute r, h values in

D) d = 6inches, h = 3inches

r = 6/2 = 3inches

Substitute r, h values in

So the possible dimensions of cone is diameter = 6 in, height = 6 in.

Option B is correct answer.

 

Comments

The formula for the volume of cone is , where r = radius and h = height.

The volume of cone is .

Multiply each side by .

From the above equation r = 3 and h = 6 respectively.

Diameter d = 2r = 2(3) = 6 inches and height h = 6 inches.

Options B is correct answer.

Answer 3

1) Slant height of squre pyramid (s)= 25m.

Lateral area of the squre pyramid (L)= 350 squre meters

Where h = height, s = slant height, a = side length, e = lateral edge length and r = a/2

Formula for volume of squre pyramid

To find volume of squre pyramid we need the values of a , h.

Formula for lateral surface area of squre pyramid

In this case L = 350 m², s = 25m

Substitute the a  value in

By the pythagorean theorem we know that

is closest to the volume of the squre pyramid.

Option H is correct answer.

Answer 4

The formula for the volume of cube , where a = side length.

The formula for the volume of hemisphere , where r = radius.

The composite figure = cube + hemisphere.

The radius of hemisphere = r and the side length of the cube a = 2r.

The volume of composite figure = volume of cube + volume of hemisphere.

.

The option (A) is correct choice.