6. if the perimeter of a semicircle is 36 cm then its radius is
7. The radius of a sphere whose surface area is 154 cm is
8. The number of cubes of side 2 cm which can be cut from a cube of side 6 cm
Answers
ANSWER 1:
- Radius of the semicircle = 11.46 cm.
GIVEN:
- Perimeter of the semicircle is 36 cm.
TO FIND:
- Radius of the semicircle.
EXPLANATION:
Perimeter of semicicle = πr units.
Perimeter of the semicircle = 36 cm.
π r = 36
r = 36 / 3.14
r = 11.46 cm
HENCE THE THE RADIUS OF THE SEMICIRCLE = 11.46 cm.
ANSWER 2:
- Radius of the sphere is 3.5 cm.
GIVEN:
- Surface area of the sphere is 154 cm².
TO FIND:
- Radius of the sphere.
EXPLANATION:
Surface area of the sphere = 4 π r² sq. units.
Surface area of the sphere = 154 cm².
4 π r² = 154
4 × 22 / 7 × r = 154
r² = 7 × 7 / 4
r² = 49/4
r = 7/2
r = 3.5 cm
HENCE THE RADIUS OF THE SPHERE = 3.5 cm.
ANSWER 3:
- 27 cubes of side 2 cm can be cut off from the cube of side 6 cm.
GIVEN:
- Cubes of side 2 cm are cut from a cube of side 6 cm.
TO FIND:
- Number of cubes which can be cut.
EXPLANATION:
Volume of cube = a³
Let volume of larger cube be a³ and the volume of smaller cube (a')³
Volume of larger cube (a³) = 6³
Volume of smaller cube [ (a')³ ] = 2³
a³ = (a')³ × n
6 × 6 × 6 = 2 × 2 × 2 × n
n = 3 × 3 × 3
n = 27
HENCE 27 CUBES CAN BE CUT OFF.
Answer 6.
Perimeter of semicircle = 1/2 × Circumference of circle
= 1/2 × 2 πr
Perimeter of semicircle = πr
→ 36 = 22/7 × r
→ 36(7)/22 = r
→ 11.45 = r
Hence the radius of the semicircle is 11.45 cm.
Answer 7.
Area of sphere = 4πr²
Substitute the known values in the above formula,
→ 154 = 4 × 22/7 × r²
→ 154(7)/22(4) = r²
→ 12.25 = r²
→ 3.5 = r
Hence, the radius of the sphere is 3.5 cm.
Answer 8.
Volume of cube of 6 cm = Volume of cube of 2 cm × n
→ 6 × 6 × 6 = 2 × 2 × 2 × n
→ 216/8 = n
→ 27
Hence, the number of cubes is 27.