Answer: Statement B is correct; the two tiles are similar because PQ:QR is 1:3 and JK:KL is also 1:3
Step-by-step explanation: The two tiles as shown in the diagram has their dimensions given according to their position on the Cartesian plane. Tile SRQP has its width at coordinates (2,2) and (4,2) which means the width spans from 2 cm to 4 cm on the x-axis, that is a length of 4 minus 2 which is 2 cm. Similarly the length is at coordinates (2,2) to (2,8) which means the length spans from 2 cm to 8 cm on the y-axis, that is a length of 8 minus 2 which is 6 cm. Therefore the dimensions of the first tile is 6 cm by 2 cm.
Similarly, we can derive the length and width of the smaller tile MLKJ, by applying the same procedure and what we would have is a tile measuring 3 cm by 1 cm.
The ratio of tile SRQP can be derived as
Ratio = 2 : 6
Ratio = 1 : 3
Also the ratio of the tile MLKJ can be derived as
Ratio = 1 : 3
Having calculated the ratio 1 : 3 for both tiles, then we can safely conclude that both are similar.
Answer:
184.43in².
Step-by-step explanation:
Total surface area of the solid = volume of the cube - the volume of the cone
For the CUBE;
Volume of the cube = L³ where L is the length of one side of the cube.
Since a cone of diameter of 6in is cut into a cube, then the length of the cube will be 6in.
Volume of the cube = 6³ = 216in³
For the CONE;
Volume of the cone = 1/3 πr²h
r is the radius of the cone = diameter/2
r = 6/2 = 3in
slant height l = 4.5in
the height h of the cone will be derived using the Pythagoras theorem.
l² = h²+r²
4.5² = h²+3²
h² = 4.5²-3²
h² = 11.25
h=√11.25
h = 3.35in
Volume of the cone = 1/3 × π × 3²× 3.35
= 31.57in³
Total surface area of the solid = 216in³-31.57in³
= 184.43in²
2 is 60, 1 is 60, 3 is 55, 4 is 120
Answer:
1:14
2:16
3:18
4:20
Step-by-step explanation:
Answer:
Option (C)
Step-by-step explanation:
From the graph attached,
In ΔABC and ΔA'B'C',
∠A ≅ ∠A'
∠B ≅ ∠B'
Therefore, ΔABC ~ ΔA'B'C'
Corresponding sides of these triangles will be proportional.
Therefore, ratio of the sides, AC : A'C' = 1 : 3 shows that image triangle A'B'C' is a dilated form of pre-image ABC with a scale factor of 3.
Option (C) will be the correct option.
