Answer to Question #138136 in Geometry for Hiroshima

Question

1. The angle of a sector is 30° and the radius is 20 cm. What is the area of the sector in sq.cm.?
2. Find the area of the segment of a circle whose diameter is 20 cm and the central angle measures 70°
3. A square is inscribed in a circle whose area is 144π, determine the perimeter of the square.
A circle has an area equal to 25π cm2. Its diameter AB coincides with one of the sides of a triangle ACB whose vertex
C lies on the circle. Triangle ACB has an area equal to 15 cm2. What is the area of the portion of the circle which is outside the triangle in cm2?
5. Find the edge of a cube if its surface area is numerically equal to its volume
6. The base of a rectangular solid is 4 m long and 3 m wide. Find the volume of the solid if its diagonal is √41 m.

Answer 1

#138136

1. 30⁰/360⁰x3.142x20x20=104.73cm²

2.(70⁰/360⁰x3.142x10x10)-(1/2x10x10xsin70⁰)=22.4cm²

3.r=12cm, length of square=16.97cm

Perimeter=16.97x4=67.88cm

4.radius of circle=5cm, diameter=10cm

Area outside the circle= (1/2x3.142x5x5)+ (39.275-24.275)= 54.275cm²

5. Volume= L³, S.A=L²x6, 6L²=L³, hence L=6cm

6. Length of base diagonal = 5m (using Pythagoras theorem).

then width will be given by applying Pythagoras 5²+x² (x is the width)=41M. solving the equation gives width=4m

Width of the solid =4m

Hence volume= 4x3x4=48m³