WBBSE Class 10 Maths Mensuration Chapter 4 Sphere Multiple Choice Questions

WBBSE Class 10 Maths Mensuration Chapter 4 Sphere Multiple Choice Questions

Example 1. The volume of a solid sphere having a radius of 2r units length is

1. \(\frac{32}{3} \pi r^3 \text { cu.u. }\)
2. \(\frac{16 \pi r^3}{3} \text { cu.u }\)
3. \(\frac{8 \pi r^3}{3} \mathrm{cu} .\)
4. \(\frac{64 \pi r^3}{3} \text { cu.u }\)

Solution: Volume = \(\frac{4}{3} \pi(2 r)^3 \text { cu unit }=\frac{32 \pi r^3}{3} \text { cu.u }\)

∴ Answer is 1. \(\frac{32}{3} \pi r^3 \text { cu.u. }\)

Example 2. If the ratio of the volumes of two solid sphere is 1: 8, the ratio of their curved surface area is

1. 1: 2
2. 1: 4
3. 1: 8
4. 1: 16

Solution: Ratio of volume = \(\frac{\frac{4}{3} \pi}{\frac{4}{3} \pi}\left(\frac{r_1^2}{r_1^2}\right)^3=\left(\frac{1}{8}\right)\)

∴ \(\frac{r_1}{r_2}=\frac{1}{2}\)

Ratio of curved surface = \(\frac{4 \pi}{4 \pi}\left(\frac{r_1}{r_2}\right)^2=\frac{1}{4}\)

∴ Answer is 2. 1: 4

Read And Learn Also WBBSE Class 10 Maths Multiple Choice Questions

Example 3. The whole surface area of a solid hemisphere with length of 7 cm radius is

1. 588 π sq. m
2. 392 π sq. m
3. 147 π sq. m
4. 98 π sq. m

Solution: Whole surface area = 3π (7)² sq. cm = 147 sq. cm

∴ Answer is 3. 147 π sq. m

Class 10 Maths Mensuration Chapter 4 Sphere MCQs

Example 4. If the ratio of curved surface areas of two solid sphere is 16: 9, the ratio of their volumes is

1. 64: 27
2. 4: 3
3. 27: 64
4. 3: 4

Solution: \(\frac{4 \pi}{4 \pi}\left(\frac{r_1}{r_2}\right)^2=\frac{16}{7}\)

or, \(\frac{r_1}{r_2}=\frac{4}{3}\)

∴ \(\frac{\frac{4}{3} \pi}{\frac{4}{3} \pi}\left(\frac{r_1}{r_2}\right)^3=\left(\frac{4}{3}\right)^3\) = 64: 27

∴ Answer is 1. 64: 27

Example 5. If numerical value of curved surface area of a solid sphere is three times of its volume the length of radius is

1. 1 unit
2. 2 unit
3. 3 unit
4. 4 unit

Solution: \(4 \pi r^2=3 \frac{4}{3} \pi r^3\) or, r = 1

∴ Answer is 1. 1 unit

Sphere Mcqs Class 10

Example 6. Volume of a sphere of radius \(\frac{r}{2}\) units will be

1. \(\frac{1}{6} \pi r^3 \text { cu. u. }\)
2. \(\frac{4}{3} \pi r^3 \text { cu. u. }\)
3. \(\frac{2}{3} \pi r^3 \text { cu. u. }\)
4. \(\frac{1}{3} \pi r^3 \text { cu. u. }\)

Solution: Volume = \(\frac{4}{3} \pi\left(\frac{r}{2}\right)^3\) cu. unit

= \(\frac{\pi r^3}{6}\) cu units

∴ Answer is 1. \(\frac{1}{6} \pi r^3 \text { cu. u. }\)

Example 7. If numerical value of curved surface area of a solid sphere Is equal to its volume, then the length of its radius is

1. 6 unit
2. 5 unit
3. 4 unit
4. 3 unit

Solution: \(4 \pi r^2=\frac{4}{3} \pi r^3\) or, r = 3

∴ Answer is 4. 3 unit

Example 8. The ratio of whole surface area of a solid sphere and solid hemisphere of same radius will be

1. 4: 3
2. 3: 4
3. 1: 2
4. None of these

Solution: Ratio = 4π (r)² : 3πr² = 4:3

∴ Answer is 1. 4: 3

Example 9. The ratio of numerical values of volume and whole surface area of a sphere is 2: 1. Numerical value of radius is

1. 5
2. 6
3. 3
4. 1

Solution: \(\frac{\frac{4}{3} \pi r^3}{4 \pi r^2}=\frac{2}{1}\)

or, \(\frac{r}{2}\) = 2, r = 6

∴ Answer is 2. 6

Class 10 Mensuration Sphere Mcqs With Answers

Example 10. Volume of a sphere is \(\frac{4}{3} \pi r^3\) πr³ cu. units. The sphere is inscribed (in) a cube. The ratio of volumes of the cube and the sphere is

1. 3: π
2. 4: π
3. 6: π
4. 8: π

Solution: Length of the side of the cube = 2r units

Ratio = (2r)³ : \(\frac{4}{3}\) πr³ = 6 : n

∴ Answer is 3. 6: