If the radius of a sphere is increased by 50%, find the percent increase in surface area. Option 1: 125% Option 2: 250% Option 3: 237.5% Option 4: 220%

Answer: 125%. Solution: Original radius = r Radius increased by 50% means new radius = r + 0.5r = 1.5r Surface area of a sphere = 4 r^2 Original surface area: A_1 = 4 r^2 New surface area with radius 1.5r: A_2 = 4(1.5r)^2 A_2 = 4 x 2.25 x r^2 A_2 = 9 r^2 Increase in surface area: Increase = 9 r^2 - 4 r^2 Increase = 5 r^2 Percent increase: Percent Increase = (Increase)/(Original) x 100 = (5 r^2)/(4 r^2) x 100 = 5/4 x 100 = 1.25 x 100 = 125 Therefore, the percent increase in surface area is 125%.

Geometry

Solids

Medium

If the radius of a sphere is increased by 50%, find the percent increase in surface area.

125%

250%

237.5%

220%

✅ Correct Option: 1

Original radius = $r$

Radius increased by 50% means new radius = $r + 0.5r = 1.5r$

Surface area of a sphere = $4\pi r^2$

Original surface area:

$A_1 = 4\pi r^2$

New surface area with radius $1.5r$ :

$A_2 = 4\pi(1.5r)^2$

$A_2 = 4\pi \times 2.25 \times r^2$

$A_2 = 9\pi r^2$

Increase in surface area:

$\text{Increase} = 9\pi r^2 - 4\pi r^2$

$\text{Increase} = 5\pi r^2$

Percent increase:

$\text{Percent Increase} = \dfrac{\text{Increase}}{\text{Original}} \times 100$

$= \dfrac{5\pi r^2}{4\pi r^2} \times 100$

$= \dfrac{5}{4} \times 100$

$= 1.25 \times 100$

$= 125$

Therefore, the percent increase in surface area is 125%.

2026: 14 May Shift 1

A cone of the height 54 cm and radius of the base of 4 cm is made up of clay. Aditya reshapes it in the form of a sphere. The radius of the sphere will be

2026: 19 May Shift 2

A rectangular block with a volume of 250 cm³ was sliced into two cubes of equal volume. How much greater (in sq.cm) is the combined surface area of the two cubes than the original surface area of the rectangular block?

2026: 30 May Shift 2

Consider the surface area of the following solids.

(A) A cylinder with a diameter of base 14 cm and height 80 cm.

(B) A cone with a radius of 7 cm and slant height 10 cm.

(D) A hemisphere with a radius of 21 cm.

Arrange the above in decreasing order.

Choose the correct answer from the options given below:

2025: 29 May Shift 1

If the length of a cuboid is increased by 20% and its breadth is decreased by 20%, then the volume of cuboid

2025: 30 May Shift 2

A flask in the shape of a right circular cone of height 36 cm is completely filled with tea. The tea is then poured into another right circular cylindrical flask whose radius is two-third of the radius of base of the circular cone. Then, the height of the tea in the cylindrical flask is

2023: 24 May Shift 3

A cuboidal slab of copper having dimensions 22 cm $\times$ 10 cm $\times$ 5 cm is melted and recasted in the form of a wire of 1 mm diameter. The wire is rubber coated at the rate of Rs. 1.50 per meter. Find the cost of rubber coating (in Rs.) Use $\pi = \frac{22}{7}$ .

If the radius of a sphere is increased by 50%, find the percent increase in surface area.

Solution

Related questions:

Keyboard Shortcuts

CUET General Test Past Year Questions (Topic-Wise)