Answer:
5. LA = 301.6 sq. cm., SA = 402.1 sq. cm.
6. LA = 377.0 sq. in., SA = 603.2 sq. in.
7. LA = 113.1 sq. cm., SA = 169.6 sq. cm.
8. LA = 502.7 sq. cm., SA = 603.2 sq. cm.
9. 396 sq. in.
Step-by-step explanation:
The lateral area is the area of all the faces, except the base(s). The surface area is the area of ALL the faces of the shape.
5.
The lateral area of a cylinder is given by the formula:
LA = 2πrh
where r is the radius and h is the height of the cylinder
So, lateral area would be 2π(4)(12) = 301.6 sq. cm.
The surface are would be the lateral area (301.6) PLUS the area of 2 of the circular bases. Circle has an area of πr^2.
So 2 bases would have area of (π(4)^2)*2=100.5
Thus, the surface area = 301.6 + 100.5 = 402.1
6.
The lateral area would be LA = 2πrh
The radius is given as 6 and height as 10. Plugging it would give us:
LA = 2πrh = 2π(6)(10) = 377.0 sq. in.
For the surface area, we would need to add the top and bottom (which are 2 identical circles with area πr^2 each) with the lateral area. So we have:
2 * (π(6)^2)
=226.2
Surface area = 377.0 + 226.2 = 603.2 sq. in.
7.
The radius of the cylinder is 3 and height is 6. We will plug them into the respective formulas.
<u>lateral area:</u>
LA = 2πrh = 2π(3)(6) = 113.1
<u>surface area:</u>
area of 2 circles (top and bottom) = (πr^2)*2 = (π(3)^2)*2 = 56.5
Surface area = 113.1 + 56.5 = 169.6
8.
diameter is given as 8, so radius is half of it. Hence, radius is 4 and height given as 20.
Plugging these values into the respective formula we will get the answer.
<u>lateral area:</u>
LA = 2πrh = 2π(4)(20) = 502.7
<u>surface area:</u>
area of both the circles (top and bottom) PLUS the lateral area of 502.7.
So, surface area = 502.7 + (πr^2)*2 = 502.7 + (π(4)^2)*2 = 603.2
9.
The frosting area of area of two rectangles (left and right) + area of two rectangles (back and front) + area of rectangle (top).
So, surface area of the frosting part = 2 (4*15) + 2(4*12) + (12)(15) = 396
