If the slant height of a cone is… - CUET UG 2025 General Test PYQ

CUET UG 2025 — General Test Geometry

2025mcqmedium

If the slant height of a cone is decreased by 15 percent and the radius of its base is increased by 20 percent, then by what percent will its curved surface area change?

Official previous-year question

Held on 27 May 2025 · Verified 13 Jul 2026.

Options

A
2 percent decrease
B
2.5 percent decrease
C
2.5 percent increase
D
2 percent increase

Did you get this right?

Solution

The curved surface area (CSA) of a cone is given by:

$\text{CSA} = \pi r l$

where $r$ is the radius of the base and $l$ is the slant height.

Let the original radius be $r$ and the original slant height be $l$ .

Original CSA $= \pi r l$

The slant height decreases by 15%, so the new slant height is 85% of the original:

New slant height $= 0.85l$

The radius increases by 20%, so the new radius is 120% of the original:

New radius $= 1.20r$

The new curved surface area is:

New CSA $= \pi \times (1.20r) \times (0.85l)$

New CSA $= \pi \times 1.20 \times 0.85 \times r \times l$

New CSA $= 1.02 \times \pi r l$

The new CSA is 1.02 times the original CSA, which represents 102% of the original.

Percentage change $= (1.02 - 1) \times 100\%$

Percentage change $= 0.02 \times 100\%$

Percentage change $= 2\%$

Since the new CSA is greater than the original, this represents a 2 percent increase.

Your note

CUET UG Geometry in other years

Geometry 2024 Geometry 2023 Geometry 2022

More CUET UG Geometry questions

Match the given areas of various solid objects with their respective formulae: | List I | List II | |---|---| | Area of solid object | Formula | | (A) Lateral surface area of a cylinder | (I) $\pi r\sqrt{r^2 + h^2}$ | | (B) Total surface area of a hemisphere | (II) $4\pi r^2$ | | (C) Lateral surface area of a cone | (III) $2\pi rh$ | | (D) Surface area of a sphere | (IV) $3\pi r^2$ | (Where, r = radius of the solid shape (or base) and h = height of the solid shape.) Choose the correct answer from the options given below:

2025easy

A solid, metallic right circular cone of radius 7 cm and height 3 cm is melted into three cubes. If the sides of two cubes are 3 cm and 5 cm, then the side of the third cube will be how much?

2025medium

The area of a rectangle whose length is 5 more than twice its width is 75 square unit. What is the perimeter of the rectangle?

2025medium

(A). The angles of depression of two ships from the top of a lighthouse are $60^\circ$ and $45^\circ$ towards the east. If the ships are $300$ meter apart, the height of the lighthouse is $150(3+\sqrt{3})$ $$\newline$ (B). If the surface area of a cube is $726 \text{ m}^2$, then its volume shall be $1331 \text{ m}^3$ $$\newline$ (C) If the ratio of diameters of two spheres is $3:5$, then the ratio of their surface area shall be $9:25$ $$\newline$$ Determine as to which of the statements given above are correct :

2025medium

If area of a square is 44 cm², find the area of the circle formed by the same perimeter.

2025medium

View all Geometry questions